[jacktoole1]

For anyone else running into the same problem, I just copied my HipChat.app in /Applications, and ran the second hipchat next to the first hipchat (you can also change the second hipchat's icon for easy distinguishment). It's not perfect (upon logout/restart it still remembers the preferences for the other instance), but it solved 90% of my hassle.

[talkingquickly]

This has been driving me crazy for months, I had one version of the old buggy Adobe Air app running and one of the new Native app. Somehow just creating a copy of the new native app just never occurred to me. You just made my day substantially better.

[JesseObrien]

You can also do in the terminal:

  hipchat --detach &

[cooper12]

Or for even any app:

    open -n /path/to/application.app

From the open man page:

    -n  Open a new instance of the application(s) even if one is already running.

[chermanowicz]

That's smart. But still, it's crazy that something like multiple organizations would require you to do this on your end. There are better options out there :)