To cram a "tweet" on Twitter in Twitter's 140 character limit using an intense level of chat-speak ; a hybrid between the terms "chat-speak" and "tweet."
One of the positive few uses for chat-speak.
Here is an example of a normally literate person using Tweetspeak in order to relay his message in under 140 characters:
"@person I'm going2have 2 bail on Noah and the Whale this weekend, man. Sorry. I would love2go,but I'm snowed under w/ an essay deadline."