TweetDeck, the popular Adobe AIR-based Twitter client, started offering a web-based version of its service in Google’s Chrome Web Store late last year. There, it quickly became one of the most popular apps in the store. Today, TweetDeck is launching a limited beta of the web-based version of TweetDeck that will also be available to users of other browsers. Specifically, TweetDeck Web will work with Chrome, Firefox 3.6 and 4, as well as Safari. Support for IE9 and Opera is coming soon.