Hi!
A forum I migrated used a lot a chat box (permanently visible) in their previous forum (phpBB + some chat box plugin, I suppose). So, the feature was asked for the migration.
The chat was implemented, but it didn’t work at all. Nobody uses it. We even added a link in the top bar:
But it didn’t change anything.
I suspect it’s because nobody wants/thinks about clicking a button to see a chat that will disappear the next time they open the forum. A poll on our forum could be a good idea though. 
Having Discourse remember the chat toggle status when closing/opening the browser could maybe make things work.
However, I’m aware that it would be difficult to implement, especially if users want to see it permanently since the chat uses a pop-up and can overlay the forum’s content.
So I absolutely don’t have a clear idea of how it could be implemented seamlessly (even in terms of layout), but if some people have an opinion about such a feature and how a community could benefit (or not!) from it, that would be cool to hear. 