I made one of these a little over a year ago, for fun:

https://chrome.google.com/webstore/detail/sitechat/affmlbhoe...

We don't store logins, messages, or logs on any DB so it's ostensibly anonymous. You can use a nickname but you can't register.

It launched to a ton of early success. Thousands of simultaneous users for a few months, then it just fizzled and died. Good luck.