diff --git a/pandas/tests/io/parser/common/test_chunksize.py b/pandas/tests/io/parser/common/test_chunksize.py
index 3d9d780a1e878..8e1e9fb6e458f 100644
--- a/pandas/tests/io/parser/common/test_chunksize.py
+++ b/pandas/tests/io/parser/common/test_chunksize.py
@@ -173,7 +173,7 @@ def test_chunks_have_consistent_numerical_type(all_parsers):
     assert result.a.dtype == float
 
 
-def test_warn_if_chunks_have_mismatched_type(all_parsers):
+def test_warn_if_chunks_have_mismatched_type(all_parsers, request):
     warning_type = None
     parser = all_parsers
     integers = [str(i) for i in range(499999)]
@@ -184,8 +184,27 @@ def test_warn_if_chunks_have_mismatched_type(all_parsers):
     if parser.engine == "c" and parser.low_memory:
         warning_type = DtypeWarning
 
-    with tm.assert_produces_warning(warning_type):
-        df = parser.read_csv(StringIO(data))
+    buf = StringIO(data)
+
+    try:
+        with tm.assert_produces_warning(warning_type):
+            df = parser.read_csv(buf)
+    except AssertionError as err:
+        # 2021-02-21 this occasionally fails on the CI with an unexpected
+        #  ResourceWarning that we have been unable to track down,
+        #  see GH#38630
+        if "ResourceError" not in str(err) or parser.engine != "python":
+            raise
+
+        # Check the main assertion of the test before re-raising
+        assert df.a.dtype == object
+
+        mark = pytest.mark.xfail(
+            reason="ResourceWarning for unclosed SSL Socket, GH#38630"
+        )
+        request.node.add_marker(mark)
+        raise
+
     assert df.a.dtype == object