Asides from the lack of given information, you should possibly evaluate your first sentence.
"... best performance for a perl-mysql chat"
I'm guessing that you intend to make this accessable from a webpage, since if this was client or telnet accessed, using a DB backend would just be silly.
In this case, I would suggest you forget about using MySQL, or any RDBMS for that matter, as a back-end to this - as performance wouldn't be particularly impressive at all... To be honest, it'd be a very strange way of going about it with this example.

merlyn has already written a good column about web chatters: December 2000
This would probably be a good way to go about this :)

JP,
-- Alexander Widdlemouse undid his bellybutton and his bum dropped off --