I'd like to see chat integrated a little more into the site for those who actively use it. Stealing the concept from Facebook, I believe it would be a nice addition to show a "chat bar" on the side of the page.
The chat bar would only show up if the following conditions are met:
You have favorited one or more chat rooms.
Your browser viewport is over a specific width.
You would always have the ability to toggle the side bar, which would be remembered on subsequent visits.
The chat bar would contain a summary of your favorite rooms, who is currently active, and a summary of the starred topics. An indicator would also appear to let you know if there are any unread messages targeting you in the chat room.
In addition, you would hear the sound notification if you are mentioned in any of your favorited chat rooms, even when they are not open.
This idea could be further improved on. Perhaps you could expand certain rooms and be able to chat from within the sidebar without having to actually enter the room, for example.
Here's a quick mockup of the idea, looking at the front Stack Overflow page:
Please excuse the same content copy and pasted a few times, this is just a conceptual mockup.