"much lighter and thinner than running Twitter through a browser interface."
However, you can run Tweetdeck in Chrome (Tweetdeck for Chrome, or ChromeDeck)
And soon they will have the chromedeck as a web app at web.tweetdeck.com, too.
This is a great achievement for the Tweetdeck team! I just hope it doesn't ruin the good things that are going on!
Maybe Tweetdeck can give Twitter a lesson or two on how to make the API work properly...