Not quite a chatbox app for the forum, but people are welcome to sign up for the Tweetfleet Slack group (character name or backstage handle if you prefer, most people are using their ingame handles) if they would like. You can do so at the signup page located here
There's a bunch of channels already made, but #lore is probably the one most here will want to hang out in. I have not made a Backstage channel but I can do so if people would prefer it.
Ignoring the majority of the features, Slack's chat channels keep records of everything said so you can read back and see what you missed even while you were offline. I believe there are mobile apps for it as well, or you can just run it in a browser tab if you prefer. So it should satisfy most of the needs of the people who want a chatbox for backstage.