Campfire like chat plugin?

I've got to write a little app at work for doctors and med students to
view a streaming video feed, and the users want the ability to have a
chat window. I've got everything else figured out, authentication, the
stream, etc. The chat feature is something I don't really know where
to start on. It does not need to be nearly as fancy as Campfire. The
only "extra" is that the chats need to be logged transcripts can be
downloaded later. Does anyone know of a plugin that might do this? Or,
I'd love to hear of some ideas you may have.

Good call. That's helpful.

Thanks, unfortunately this is for a medical school and there is the
slightest chance that HIPAA type info could be chatted over. Yes, the
docs know they shouldn't but they talk about patients via unencrypted
email when they aren't still too. So having chats stored on an
external site is a no go.