If you got here by clicking "The Corner Office" at the bottom of one of my tweets, thank you! In order to get the free software to brand your own tweets, please visit my friend Kay Ballard's blog, New Media Martini.
Be aware that this software runs on Adobe AIR. I understand there is an AIR environment available for Windows, Mac, and Linux, so you should be covered.
While the software itself is free of monetary charge, you will be asked for your email address twice: first by New Media International (they won't bug you much--just let you know when new products or websites are launching); then by the publisher of the software. I think it's worth it.
UPDATE 2010/06/23: I've been told the publisher of the free TweetBrand software has stopped supporting it. If you follow the steps, you may or may not be able to download and install it, but there will be no upgrades.