Converse.js is a free and open source chat client that runs in your browser. It can be integrated into any website. Similar to Facebook chat but it also supports multi-user chatrooms.
Converse.js can connect to any accessible XMPP/Jabber server, either from a public provider such as jabber.org, or one you have set up yourself. It’s possible to enable single-site-login, whereby users already authenticated in your website will also automatically be logged in on the chat server.