As you are already familiar with JavaScript, I would recommend a combination of Node.js, Now.js and node-irc.
Node.js is an application that enables you to run JavaScript server-side and to develop web-applications very fast.
Now.js is a library for Node.js that enables you to RPC between client and server. You can just call a function on the server from your client application and vice-versa; their developers guide is in fact a web chat ;)
node-irc is also a library for node.js that enables you to easily create an IRC client.
Combine these three and you get a very nice, very easy self-coded web chat. For the browser interface, there are many possibilities, including application frameworks like ExtJS, JQueryUI, KendoUI or something easier.