I\'m doing research for making a chat based app for the iPhone (it\'s not really text chat in the regular sense, but the principles are the same).
Maximum 6 people
I think you can either go with push notifications, or XMPP (Jabber) server.
XMPP will allow your iphone app to receive data even when in the background using the new multitasking features (listening for a socket), and i'm pretty sure you should find ready to use servers for LAMP (or at least open source implementations).
Note that the iOS4 multitasking API doesn't support polling in the background, so your only other option should be push notifications. If you're new to push notifications, you can maybe use a service like Urban Airship that might make the process easier.
XMPP sounds good for you idea, i think this is the best technology for Chat. It alos works great in iOS apps.
Maybe this code sample will be helpful to start using XMPP in iOS app - look at this QuickBlox Chat code sample. It demonstrates how to integrate 1-1 Chat, Chat in room into your android application. Also there is guide how it works. I think there will be no problem to integrate it into your application. Otherwise - Comments system below allows to ask any question you want and get fast answer.
Also there is Demo video http://www.youtube.com/watch?feature=player_embedded&v=SncQaJBBW_0 how this Chat works.
In my opinion the best solution is socket, but you say that you can't implement the server side for this.
You could also implement it with push notifications. You can receive the push also when your app is running and send all the data you need inside the push. Usually chat messages are short...
If you don't want to mess with push notifications on the server then the only thing left, as long as I know, is the polling.