I'd suggest using IRC through Mibbit
http://www.mibbit.com/. It's easy to set up on a website, and has full IRC features, a webchat client and PHPbb integration
http://wiki.mibbit.com/index.php/PhpBB_integration. It's free and ad-supported, with Mibbit hosting the ads (also everything else), so it shouldn't be a strain on server resources. It also means any other methods of connecting to IRC that members use would still work.