Update: Despite a number of people talking about it on Twitter, it appears that this is not an official Twitter button. How do we know? Twitter engineer Dustin Diaz responded in our comments:
This has to be some sort of extension (maybe Bitly? We don't know) - this is not found in our code source.
We've reached out to Twitter officially, but have yet to hear back. But I see no reason to not go with Diaz here. So, sorry for getting everyone all excited! It does appear that some extension which multiple users have installed is causing this button to appear — we're still trying to figure out which one.
Previously: For as great as Twitter's website is now, there's been one big glaring problem for many people using it: link shortening. Unbelievably, Twitter.com has not offered a way to shorten links either automatically or manually. You had to do it yourself and then paste those shortened links in. Well, good news, it looks like that's finally about to change.
As the site Gizable first spotted, Twitter today was briefly testing a "Shorten" button next to the standard "Tweet" button on the website. Several other Twitter users have reported seeing this button as well before it vanished. And Gizable's @AndrewBrackin even grabbed the screenshot above.
Another user notes that it was using Bit.ly rather than Twitter's own t.co address that they use on their other clients.
Update 2: Aha! It is Bit.ly. Their Chrome extension does this as an option.