You'll at least need to sign up for Dreamhost PS - both to be able to listen on a port and also to allow you to run a persistent server process.
Under a regular shared account, you can do neither.
You should be able to have your users use chat without having to do either, though. Have you looked into Jabber or some other chat solution that uses regular http?
What are [color=#CC0000]50DISK50[/color], [color=#CC0000]3DOM50[/color], and [color=#CC0000]1IP1DOM50[/color]?
They're Dreamhost coupons!