I'd also at the same time recommend one with AJAX (or use PHP Live Support and have it integrated with AJAX.) But then again, make sure you ALERT your customers/clients if they don't have JavaScript enabled then the chat will not work.
'Em, as far as recommendation... let's see,
http://www.helpcenterlive.com is a good FREE software that I believe uses AJAX. Only issue with it is that the source is open code so it may be somewhat bad to use (unless you encode it... that's the strongest belief I think can protect software. Its de-cryptable, but could get whoever de-crypts it into very high legal troubles, even if it isn't copywritten.) And plus, I am not sure, but I think its $50.00 for the Windows Desktop Client. Don't quote me on that, but check the site and double-check.