Update: I installed ChatSecure on my iPad and it's very easy to set up. So easy in fact that I'm thinking there must be something wrong with it, because otherwise it would probably be recommended more often in these types of threads...
One of the things that seems problematic is that the background session expires after a few minutes, so if someone tries to just randomly message you, chances are you won't be logged in, so this can't be a replacement for IM.