You would probably need a dedicated server to do that. You need some sort of IRC Server software installed like ConferenceRoom from www.webmaster.com. If you are using linux there is probably cheaper ones out there but I don't know linux well enough to tell you.
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Before you go with this solution though (as it requires a lot of time on your part for maintenance, depending on server usage) you should consider if creating a channel on an already popular network such as EFnet or Undernet would be sufficient for you needs. If you really want to run your own system, a Java-based system which works easily on your website might also be a nice and easy solution for you if you are not too much depending on such a chat system.