Our chat pages do something pretty great: when something lands in our inbox, we'll get a notification about it and the inbox link will light up in blue (or whatever colour your theme is).
What it doesn't do and probably should is listen out for when I've finally checked my inbox and it's been emptied. At that point, the inbox link should return to its regular colour.
At the moment when I get a message, I'll check my inbox. Then half an hour later I might have occasion to scroll to the top of the chat page (maybe to see who's there or click a link up top), see the inbox link lit up, and go: "Oh! New message!" — when there haven't been any since, it's just still lit up. Repeat maybe a couple of times until I have cause to leave the window or just refresh the chat page so that I quit doing this in repeat.