Before you start to think about implementation details like the communication between the client (browser) and the chat server you have to decide what your chat server will be. Of course you can decide to roll your own and also build it into the ASP.NET website itself eventhough I don't advocate that procedure.
Before embarking on this you further need to ask yourself a few questions. Here are a some just to get you started:
1. How many users will my system have
2. How long is a tolerable delay in the display of responses from a chatting partner.
3. Am I really willing to program a chat or will I use an existing platform.
Once you've nailed down your requirements it will be easier to start making the right decisions. Maybe AJAX (Pull) isn't the way to go at all and
Comet[
^] would be a better choice, but as I said before you better start by laying out your requirements first.
Cheers,
Manfred