Add chat widget in the docs

Inspired from the cats documentation

Author: OlivierBlanvillain

doc-tool/resources/_layouts/doc-page.html

@@ -8,6 +8,13 @@
 
 {% include "toolbar" %}
 
+<script>
+  ((window.gitter = {}).chat = {}).options = {
+    room: 'lampepfl/dotty'
+  };
+</script>
+<script src="https://sidecar.gitter.im/dist/sidecar.v1.js" async defer></script>
+
 <div id="content-wrapper">
     {% assign sidebarTop = "75px" %}
     {% include "sidebar" %}