BeeJive chat client for iphone.. Hands down! I had it on my blackberry and LOVED it. Their web based client is really nice, minus all the limitations.
Agreed, a native Chat/IM Client that is able to also run in the background
MobileChat v223 (released yesterday) flat out rocks.
Agreed, this is an awesome app, but it is still too unreliable for me. Personally, I have connection issues with it say if I want to go watch some YouTube videos or browse some pages on Safari, I find that when I come back to this app that I have lost connection - even while on WiFi, and the WiFi keep-alive setting turned on in the app itself. However, if I just start it up and put my phone in sleep mode, it works great and I still receive messages and get notified as I receive them.
Whether the SDK has the potential to deliver this sort of app, or if it is just a limitation of the phone I don't know...one can hope though.