Well, with the help of Apache, I created the poor man's web chat. And there's also a standalone web version for the doctor, which you could mutate into a chat server pretty easily.

But if you want concurrency, look at POE. Pretty easy to "appear" to do things simultaneously there, sharing the data structures needed. In fact, there's already an IRC server framework there, so you could use standard IRC clients with your "server".

If you insist on coding from scratch, you can have your child processes communicate via some lightweight database, like DBM::Deep or DBD::SQLite. It'd be pretty simple to write a classic "fork on accept" server that then uses the database to keep in touch with other children to share the chat info. Probably have to use a timed-out read loop to go check the database from time to time.