diff --git a/.gitignore b/.gitignore
index 96b1f945870de..a59f2843c365a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -62,6 +62,8 @@ dist
 coverage.xml
 coverage_html_report
 *.pytest_cache
+# hypothesis test database
+.hypothesis/
 
 # OS generated files #
 ######################
diff --git a/ci/appveyor-27.yaml b/ci/appveyor-27.yaml
index 114dcfb0c6440..6843c82236a35 100644
--- a/ci/appveyor-27.yaml
+++ b/ci/appveyor-27.yaml
@@ -28,3 +28,4 @@ dependencies:
   - pytest
   - pytest-xdist
   - moto
+  - hypothesis>=3.58.0
diff --git a/ci/appveyor-36.yaml b/ci/appveyor-36.yaml
index 63e45d0544ad9..47b14221bb34b 100644
--- a/ci/appveyor-36.yaml
+++ b/ci/appveyor-36.yaml
@@ -25,3 +25,4 @@ dependencies:
   - cython>=0.28.2
   - pytest
   - pytest-xdist
+  - hypothesis>=3.58.0
diff --git a/ci/check_imports.py b/ci/check_imports.py
index 3f09290f8c375..19e48b659617f 100644
--- a/ci/check_imports.py
+++ b/ci/check_imports.py
@@ -9,6 +9,7 @@
     'html5lib',
     'ipython',
     'jinja2'
+    'hypothesis',
     'lxml',
     'numexpr',
     'openpyxl',
diff --git a/ci/circle-27-compat.yaml b/ci/circle-27-compat.yaml
index 5e9842f4742c5..5dee6b0c8ed07 100644
--- a/ci/circle-27-compat.yaml
+++ b/ci/circle-27-compat.yaml
@@ -26,3 +26,4 @@ dependencies:
     - html5lib==1.0b2
     - beautifulsoup4==4.2.1
     - pymysql==0.6.0
+    - hypothesis>=3.58.0
diff --git a/ci/circle-35-ascii.yaml b/ci/circle-35-ascii.yaml
index 745678791458d..281ed59e2deff 100644
--- a/ci/circle-35-ascii.yaml
+++ b/ci/circle-35-ascii.yaml
@@ -11,3 +11,5 @@ dependencies:
   # universal
   - pytest
   - pytest-xdist
+  - pip:
+    - hypothesis>=3.58.0
diff --git a/ci/circle-36-locale.yaml b/ci/circle-36-locale.yaml
index 091a5a637becd..59c8818eaef1e 100644
--- a/ci/circle-36-locale.yaml
+++ b/ci/circle-36-locale.yaml
@@ -31,3 +31,5 @@ dependencies:
   - pytest
   - pytest-xdist
   - moto
+  - pip:
+    - hypothesis>=3.58.0
diff --git a/ci/circle-36-locale_slow.yaml b/ci/circle-36-locale_slow.yaml
index 649f93f7aa427..7e40bd1a9979e 100644
--- a/ci/circle-36-locale_slow.yaml
+++ b/ci/circle-36-locale_slow.yaml
@@ -32,3 +32,5 @@ dependencies:
   - pytest
   - pytest-xdist
   - moto
+  - pip:
+    - hypothesis>=3.58.0
diff --git a/ci/environment-dev.yaml b/ci/environment-dev.yaml
index f66a831aae0f5..f3323face4144 100644
--- a/ci/environment-dev.yaml
+++ b/ci/environment-dev.yaml
@@ -7,6 +7,7 @@ dependencies:
   - NumPy
   - flake8
   - flake8-comprehensions
+  - hypothesis>=3.58.0
   - moto
   - pytest>=3.6
   - python-dateutil>=2.5.0
diff --git a/ci/requirements_dev.txt b/ci/requirements_dev.txt
index a50a4dcd63508..68fffe5d0df09 100644
--- a/ci/requirements_dev.txt
+++ b/ci/requirements_dev.txt
@@ -4,6 +4,7 @@ Cython>=0.28.2
 NumPy
 flake8
 flake8-comprehensions
+hypothesis>=3.58.0
 moto
 pytest>=3.6
 python-dateutil>=2.5.0
diff --git a/ci/travis-27-locale.yaml b/ci/travis-27-locale.yaml
index 73ab424329463..aca65f27d4187 100644
--- a/ci/travis-27-locale.yaml
+++ b/ci/travis-27-locale.yaml
@@ -22,6 +22,7 @@ dependencies:
   # universal
   - pytest
   - pytest-xdist
+  - hypothesis>=3.58.0
   - pip:
     - html5lib==1.0b2
     - beautifulsoup4==4.2.1
diff --git a/ci/travis-27.yaml b/ci/travis-27.yaml
index 9c0347de9adfb..a921bcb46dba4 100644
--- a/ci/travis-27.yaml
+++ b/ci/travis-27.yaml
@@ -45,6 +45,7 @@ dependencies:
   - pytest
   - pytest-xdist
   - moto
+  - hypothesis>=3.58.0
   - pip:
     - backports.lzma
     - cpplint
diff --git a/ci/travis-35-osx.yaml b/ci/travis-35-osx.yaml
index fff7acc64d537..797682bec7208 100644
--- a/ci/travis-35-osx.yaml
+++ b/ci/travis-35-osx.yaml
@@ -25,3 +25,4 @@ dependencies:
   - pytest-xdist
   - pip:
     - python-dateutil==2.5.3
+    - hypothesis>=3.58.0
diff --git a/ci/travis-36-doc.yaml b/ci/travis-36-doc.yaml
index abb0426dbe08e..9cbc46d0a70d7 100644
--- a/ci/travis-36-doc.yaml
+++ b/ci/travis-36-doc.yaml
@@ -10,6 +10,7 @@ dependencies:
   - fastparquet
   - feather-format
   - html5lib
+  - hypothesis>=3.58.0
   - ipykernel
   - ipython
   - ipywidgets
diff --git a/ci/travis-36-numpydev.yaml b/ci/travis-36-numpydev.yaml
index 038c6537622dd..aba28634edd0d 100644
--- a/ci/travis-36-numpydev.yaml
+++ b/ci/travis-36-numpydev.yaml
@@ -8,6 +8,7 @@ dependencies:
   # universal
   - pytest
   - pytest-xdist
+  - hypothesis>=3.58.0
   - pip:
     - "git+git://github.com/dateutil/dateutil.git"
     - "-f https://7933911d6844c6c53a7d-47bd50c35cd79bd838daf386af554a83.ssl.cf2.rackcdn.com"
diff --git a/ci/travis-36-slow.yaml b/ci/travis-36-slow.yaml
index f6738e3837186..3157ecac3a902 100644
--- a/ci/travis-36-slow.yaml
+++ b/ci/travis-36-slow.yaml
@@ -28,3 +28,4 @@ dependencies:
   - pytest
   - pytest-xdist
   - moto
+  - hypothesis>=3.58.0
diff --git a/ci/travis-36.yaml b/ci/travis-36.yaml
index 7eceba76cab96..990ad0fe87dd6 100644
--- a/ci/travis-36.yaml
+++ b/ci/travis-36.yaml
@@ -41,6 +41,7 @@ dependencies:
   - pytest-xdist
   - pytest-cov
   - moto
+  - hypothesis>=3.58.0
   - pip:
     - brotlipy
     - coverage
diff --git a/ci/travis-37.yaml b/ci/travis-37.yaml
index 1dc2930bf7287..4f2138d8555e3 100644
--- a/ci/travis-37.yaml
+++ b/ci/travis-37.yaml
@@ -12,3 +12,4 @@ dependencies:
   - pytz
   - pytest
   - pytest-xdist
+  - hypothesis>=3.58.0
diff --git a/doc/source/contributing.rst b/doc/source/contributing.rst
index 625df2806add7..60bfd07961b38 100644
--- a/doc/source/contributing.rst
+++ b/doc/source/contributing.rst
@@ -820,6 +820,46 @@ Tests that we have ``parametrized`` are now accessible via the test name, for ex
    test_cool_feature.py::test_series[int8] PASSED
 
 
+.. _using-hypothesis:
+
+Using ``hypothesis``
+~~~~~~~~~~~~~~~~~~~~
+
+Hypothesis is a library for property-based testing.  Instead of explicitly
+parametrizing a test, you can describe *all* valid inputs and let Hypothesis
+try to find a failing input.  Even better, no matter how many random examples
+it tries, Hypothesis always reports a single minimal counterexample to your
+assertions - often an example that you would never have thought to test.
+
+See `Getting Started with Hypothesis <https://hypothesis.works/articles/getting-started-with-hypothesis/>`_
+for more of an introduction, then `refer to the Hypothesis documentation
+for details <https://hypothesis.readthedocs.io/en/latest/index.html>`_.
+
+.. code-block:: python
+
+    import json
+    from hypothesis import given, strategies as st
+
+    any_json_value = st.deferred(lambda: st.one_of(
+        st.none(), st.booleans(), st.floats(allow_nan=False), st.text(),
+        st.lists(any_json_value), st.dictionaries(st.text(), any_json_value)
+    ))
+
+    @given(value=any_json_value)
+    def test_json_roundtrip(value):
+        result = json.loads(json.dumps(value))
+        assert value == result
+
+This test shows off several useful features of Hypothesis, as well as
+demonstrating a good use-case: checking properties that should hold over
+a large or complicated domain of inputs.
+
+To keep the Pandas test suite running quickly, parametrized tests are
+preferred if the inputs or logic are simple, with Hypothesis tests reserved
+for cases with complex logic or where there are too many combinations of
+options or subtle interactions to test (or think of!) all of them.
+
+
 Running the test suite
 ----------------------
 
diff --git a/doc/source/install.rst b/doc/source/install.rst
index 08be1960eb957..4640da8b8239a 100644
--- a/doc/source/install.rst
+++ b/doc/source/install.rst
@@ -202,7 +202,8 @@ pandas is equipped with an exhaustive set of unit tests, covering about 97% of
 the code base as of this writing. To run it on your machine to verify that
 everything is working (and that you have all of the dependencies, soft and hard,
 installed), make sure you have `pytest
-<http://docs.pytest.org/en/latest/>`__ >= 3.6 and run:
+<http://docs.pytest.org/en/latest/>`__ >= 3.6 and `Hypothesis
+<https://hypothesis.readthedocs.io/>`__ >= 3.58, then run:
 
 ::
 
diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 32085332caf40..3e22084d98234 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -729,6 +729,7 @@ Build Changes
 ^^^^^^^^^^^^^
 
 - Building pandas for development now requires ``cython >= 0.28.2`` (:issue:`21688`)
+- Testing pandas now requires ``hypothesis>=3.58`` (:issue:22280).  You can find `the Hypothesis docs here <https://hypothesis.readthedocs.io/en/latest/index.html>`_, and a pandas-specific introduction :ref:`in the contributing guide <using-hypothesis>` .
 -
 
 Other
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 94c07bc09267f..a49bab31f0bc8 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -450,3 +450,37 @@ def mock():
         return importlib.import_module("unittest.mock")
     else:
         return pytest.importorskip("mock")
+
+
+# ----------------------------------------------------------------
+# Global setup for tests using Hypothesis
+
+from hypothesis import strategies as st
+
+# Registering these strategies makes them globally available via st.from_type,
+# which is use for offsets in tests/tseries/offsets/test_offsets_properties.py
+for name in 'MonthBegin MonthEnd BMonthBegin BMonthEnd'.split():
+    cls = getattr(pd.tseries.offsets, name)
+    st.register_type_strategy(cls, st.builds(
+        cls,
+        n=st.integers(-99, 99),
+        normalize=st.booleans(),
+    ))
+
+for name in 'YearBegin YearEnd BYearBegin BYearEnd'.split():
+    cls = getattr(pd.tseries.offsets, name)
+    st.register_type_strategy(cls, st.builds(
+        cls,
+        n=st.integers(-5, 5),
+        normalize=st.booleans(),
+        month=st.integers(min_value=1, max_value=12),
+    ))
+
+for name in 'QuarterBegin QuarterEnd BQuarterBegin BQuarterEnd'.split():
+    cls = getattr(pd.tseries.offsets, name)
+    st.register_type_strategy(cls, st.builds(
+        cls,
+        n=st.integers(-24, 24),
+        normalize=st.booleans(),
+        startingMonth=st.integers(min_value=1, max_value=12)
+    ))
diff --git a/pandas/tests/tseries/offsets/test_offsets_properties.py b/pandas/tests/tseries/offsets/test_offsets_properties.py
new file mode 100644
index 0000000000000..f19066ba76b20
--- /dev/null
+++ b/pandas/tests/tseries/offsets/test_offsets_properties.py
@@ -0,0 +1,104 @@
+# -*- coding: utf-8 -*-
+"""
+Behavioral based tests for offsets and date_range.
+
+This file is adapted from https://github.com/pandas-dev/pandas/pull/18761 -
+which was more ambitious but less idiomatic in its use of Hypothesis.
+
+You may wish to consult the previous version for inspiration on further
+tests, or when trying to pin down the bugs exposed by the tests below.
+"""
+
+import pytest
+from hypothesis import given, assume, strategies as st
+from hypothesis.extra.pytz import timezones as pytz_timezones
+from hypothesis.extra.dateutil import timezones as dateutil_timezones
+
+import pandas as pd
+
+from pandas.tseries.offsets import (
+    MonthEnd, MonthBegin, BMonthEnd, BMonthBegin,
+    QuarterEnd, QuarterBegin, BQuarterEnd, BQuarterBegin,
+    YearEnd, YearBegin, BYearEnd, BYearBegin,
+)
+
+# ----------------------------------------------------------------
+# Helpers for generating random data
+
+gen_date_range = st.builds(
+    pd.date_range,
+    start=st.datetimes(
+        # TODO: Choose the min/max values more systematically
+        min_value=pd.Timestamp(1900, 1, 1).to_pydatetime(),
+        max_value=pd.Timestamp(2100, 1, 1).to_pydatetime()
+    ),
+    periods=st.integers(min_value=2, max_value=100),
+    freq=st.sampled_from('Y Q M D H T s ms us ns'.split()),
+    tz=st.one_of(st.none(), dateutil_timezones(), pytz_timezones()),
+)
+
+gen_random_datetime = st.datetimes(
+    min_value=pd.Timestamp.min.to_pydatetime(),
+    max_value=pd.Timestamp.max.to_pydatetime(),
+    timezones=st.one_of(st.none(), dateutil_timezones(), pytz_timezones())
+)
+
+# The strategy for each type is registered in conftest.py, as they don't carry
+# enough runtime information (e.g. type hints) to infer how to build them.
+gen_yqm_offset = st.one_of(*map(st.from_type, [
+    MonthBegin, MonthEnd, BMonthBegin, BMonthEnd,
+    QuarterBegin, QuarterEnd, BQuarterBegin, BQuarterEnd,
+    YearBegin, YearEnd, BYearBegin, BYearEnd
+]))
+
+
+# ----------------------------------------------------------------
+# Offset-specific behaviour tests
+
+
+# Based on CI runs: Always passes on OSX, fails on Linux, sometimes on Windows
+@pytest.mark.xfail(strict=False, reason='inconsistent between OSs, Pythons')
+@given(gen_random_datetime, gen_yqm_offset)
+def test_on_offset_implementations(dt, offset):
+    assume(not offset.normalize)
+    # check that the class-specific implementations of onOffset match
+    # the general case definition:
+    #   (dt + offset) - offset == dt
+    compare = (dt + offset) - offset
+    assert offset.onOffset(dt) == (compare == dt)
+
+
+@pytest.mark.xfail(strict=True)
+@given(gen_yqm_offset, gen_date_range)
+def test_apply_index_implementations(offset, rng):
+    # offset.apply_index(dti)[i] should match dti[i] + offset
+    assume(offset.n != 0)  # TODO: test for that case separately
+
+    # rng = pd.date_range(start='1/1/2000', periods=100000, freq='T')
+    ser = pd.Series(rng)
+
+    res = rng + offset
+    res_v2 = offset.apply_index(rng)
+    assert (res == res_v2).all()
+
+    assert res[0] == rng[0] + offset
+    assert res[-1] == rng[-1] + offset
+    res2 = ser + offset
+    # apply_index is only for indexes, not series, so no res2_v2
+    assert res2.iloc[0] == ser.iloc[0] + offset
+    assert res2.iloc[-1] == ser.iloc[-1] + offset
+    # TODO: Check randomly assorted entries, not just first/last
+
+
+@pytest.mark.xfail(strict=True)
+@given(gen_yqm_offset)
+def test_shift_across_dst(offset):
+    # GH#18319 check that 1) timezone is correctly normalized and
+    # 2) that hour is not incorrectly changed by this normalization
+    # Note that dti includes a transition across DST boundary
+    dti = pd.date_range(start='2017-10-30 12:00:00', end='2017-11-06',
+                        freq='D', tz='US/Eastern')
+    assert (dti.hour == 12).all()  # we haven't screwed up yet
+
+    res = dti + offset
+    assert (res.hour == 12).all()
diff --git a/pandas/tests/tseries/offsets/test_ticks.py b/pandas/tests/tseries/offsets/test_ticks.py
index 24033d4ff6cbd..914d61a18ee11 100644
--- a/pandas/tests/tseries/offsets/test_ticks.py
+++ b/pandas/tests/tseries/offsets/test_ticks.py
@@ -6,6 +6,7 @@
 
 import pytest
 import numpy as np
+from hypothesis import given, assume, example, strategies as st
 
 from pandas import Timedelta, Timestamp
 from pandas.tseries import offsets
@@ -35,6 +36,45 @@ def test_delta_to_tick():
     assert (tick == offsets.Day(3))
 
 
+@pytest.mark.parametrize('cls', tick_classes)
+@example(n=2, m=3)
+@example(n=800, m=300)
+@example(n=1000, m=5)
+@given(n=st.integers(-999, 999), m=st.integers(-999, 999))
+def test_tick_add_sub(cls, n, m):
+    # For all Tick subclasses and all integers n, m, we should have
+    # tick(n) + tick(m) == tick(n+m)
+    # tick(n) - tick(m) == tick(n-m)
+    left = cls(n)
+    right = cls(m)
+    expected = cls(n + m)
+
+    assert left + right == expected
+    assert left.apply(right) == expected
+
+    expected = cls(n - m)
+    assert left - right == expected
+
+
+@pytest.mark.parametrize('cls', tick_classes)
+@example(n=2, m=3)
+@given(n=st.integers(-999, 999), m=st.integers(-999, 999))
+def test_tick_equality(cls, n, m):
+    assume(m != n)
+    # tick == tock iff tick.n == tock.n
+    left = cls(n)
+    right = cls(m)
+    assert left != right
+    assert not (left == right)
+
+    right = cls(n)
+    assert left == right
+    assert not (left != right)
+
+    if n != 0:
+        assert cls(n) != cls(-n)
+
+
 # ---------------------------------------------------------------------
 
 
@@ -200,21 +240,8 @@ def test_tick_zero(cls1, cls2):
 
 @pytest.mark.parametrize('cls', tick_classes)
 def test_tick_equalities(cls):
-    assert cls(3) == cls(3)
     assert cls() == cls(1)
 
-    # not equals
-    assert cls(3) != cls(2)
-    assert cls(3) != cls(-3)
-
-
-@pytest.mark.parametrize('cls', tick_classes)
-def test_tick_operators(cls):
-    assert cls(3) + cls(2) == cls(5)
-    assert cls(3) - cls(2) == cls(1)
-    assert cls(800) + cls(300) == cls(1100)
-    assert cls(1000) - cls(5) == cls(995)
-
 
 @pytest.mark.parametrize('cls', tick_classes)
 def test_tick_offset(cls):
@@ -226,11 +253,9 @@ def test_compare_ticks(cls):
     three = cls(3)
     four = cls(4)
 
-    # TODO: WTF?  What is this range(10) supposed to do?
-    for _ in range(10):
-        assert three < cls(4)
-        assert cls(3) < four
-        assert four > cls(3)
-        assert cls(4) > three
-        assert cls(3) == cls(3)
-        assert cls(3) != cls(4)
+    assert three < cls(4)
+    assert cls(3) < four
+    assert four > cls(3)
+    assert cls(4) > three
+    assert cls(3) == cls(3)
+    assert cls(3) != cls(4)
diff --git a/pandas/util/_tester.py b/pandas/util/_tester.py
index d18467f17ec5b..aad2f00fa0478 100644
--- a/pandas/util/_tester.py
+++ b/pandas/util/_tester.py
@@ -12,6 +12,10 @@ def test(extra_args=None):
         import pytest
     except ImportError:
         raise ImportError("Need pytest>=3.0 to run tests")
+    try:
+        import hypothesis  # noqa
+    except ImportError:
+        raise ImportError("Need hypothesis>=3.58 to run tests")
     cmd = ['--skip-slow', '--skip-network']
     if extra_args:
         if not isinstance(extra_args, list):