There's no built in functionality to do this. There may be a plugin but I don't know of one.
UNSOLVED Browsing Users for chats
Hello. I am aware of the browsing users plugin and have it installed. What I'm wondering is if there is a similar plugin that would be for the chat windows so you can see who's looking and typing, kinda like Snapchat. Does anyone know?
@dunlix is indeed very much needed