When I started on this site, although I saw Chat mentioned here and there I wasn't fully aware how to find it and use it. I think there could be better signposting for new users of what advantages chat offers, how it can be used, and what rooms are available to math stackexchange users.
Even now after over a year using the site, I discover new chat rooms and features. I think a page describing some of the most important chat resources would be a good improvement to math.stackexchange. This page might be signposted from the first post screen, and from various issues such as question closed, deleted, downvoted etc.