Similar to the popular disposible chat websites (check 7 Free Disposable Chat Systems For Instant Communication), Anologue is an impressive one which is open source.

It works by simply clicking on a "new room" link and the application instantly creates a chat room with a unique URL where you can invite others.

The application is totally Ajaxed, built with PHP and uses the Lithium Framework, CouchDB and jQuery.

And, if you don't prefer to install your own, you can still use Anologue as the hosted version is free for everyone.

Requirements: PHP 5.3+, CouchDB, rad-dev account
Website: http://anologue.com/
Download: http://rad-dev.org/lithium_anologue