You can insert a chat module on your site by creating an account with a site that provides this kind of service.
We recommend you this site: http://www.meebome.com/
From there (registration is free) you'll be able to easily create a custom module for chatting, choosing its size and colours.
Then (after registering or entering your username and password if you're already registered) you'll be given a code that you'll just have to insert into the block you want the chat module to show up, using the source code
mode in the block itself.
Should you need more space in your page to host the chat module, you could decide not to show the left column