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What about players that are using the chat for a long time? Eventually they'll just see their chat slowing down and finally stop updating even if they're not idle.
Your timing is a good start, but I believe you'll find that your first step (once per second) will be too hard of a hit for the performance it offers. You can really get away with once every 2 seconds here (once every 3 if you want to push the envelope). You can easily tweak this as needed.
I started a php chat project using jquery, then found mibbit and abandoned the idea (too much work for a service I can get for free elsewhere). I could provide you with at least part of my code if you'd like.
The others are correct 1 second polling intervals will kill a server If you are going to go with polling at that rate make sure you have some sort of blocking mechanism coded into your polling rates. Meaning set a variable called something like block to 1 when you send out your AJAX request, reset it to zero when the request comes back. The biggest thing is to check that block the next time you send out the next request to make sure you got a reply back from the server, if not an internal queue at the browser starts to pile up and bad things happen