If someone chats you and you haven't viewed it yet, would be cool to have it flash in the title bar in case you're in another tab. Back and forth between Chat from User and the actual title of the page you're on.
I'm using NodeBB as an interface for an app, more like a crowdsourcing hub. The forum is okay, but sometimes the communication is more dynamic and people have to either speak on the phone, use other apps or meet in person.
For new forums or for forums with small user base, a cross-forum chat room would be very engaging.
For the UI I'm imagining something like DC++ looked like in the old days.
This idea fits in different scenarios. At least in mine it does. The chat room would be an extension of the forum.