Now, a startup open source project called Status.net. They are offering two solutions:
- Hosted solution. (takes time to activate)
- Open Source download
I went ahead and tried the second one. The code is written in PHP and MySQL and is fairly easy to install, took couple of seconds. And this is the result: DEMO
The application looks fairly looks like Twitter feature wise. You can give it a try by signing-up there.
Let us know what you think.