It is not possible to create One-to-one chat with AJAX. Well it is, I did it in phpbb SN but it only worked on small boards with not so many online users. If you have many online users on your forum, server would go crazy.
If you want the "facebook chat" you should do it how facebook and google (gTalk) did it. Use XMPP.
1. you need to install an XMPP server on your server (I have good experience with OpenFire)
3. extension also has to use bosh server for prebinding, so that user does not have to log in to chat manually and connection is not lost after page reload.
I am developing pretty big "facebook like" social network for a client (budget is about 100 000 €) and I also do it this was. I use OpenFire, ConverseJS and XMPPHP for bosh server. This solution handles many simultaneously online users and has all the features like 'Typing...', accepting contacts, statuses (online, offline, busy, away), text statuses, logout etc...
When you use XMPP you can also log in to this chat using any XMPP client such as Pidgin, Digsby etc.. There are also many xmpp clients on for smartphones so no problem with that..