Update: Peer Guardian seemed to be the culprit. It was apparently running in the background on my iMac. I've no idea why it only interefered with HipChat and not any of the other many apps that I've run (GotoMeeting, Logmein, Socialcast, Yammer, GTalk, etc)
Congratulations to HipChat on being the first chat application that I can remember that has ever reported firewall issues on my computer. Can you imagine rolling this out to 10 to 20 (or more) people and having to debug everyone's firewall issues?
I can't.
Uninstalled. Test drive over.