Google publicly unveiled the Chrome Web Store a week ago. Looking at the most popular apps in the U.S. by weekly install numbers, it looks like TweetDeck has fast risen to the most prominent spot on the list, as relayed by the startup’s founder Iain Dodsworth earlier today.

With about 102,500 weekly installs at the time of writing, TweetDeck thus beats NYTimes, whose app has seen approximately 87,700 weekly installs to date, roughly seven days in.

So where are the Google services? Right behind the TweetDeck and the NY Times, it appears.

The list of top 10 most popular apps on the Chrome Web Store includes Google Calendar, Google Books, Google Docs, Google Reader, Gmail, Google Maps and YouTube.

Granted, most of Google’s ‘apps’ are mere links to the respective Web-based services, whereas ‘ChromeDeck’ is an actual app, but still.

Springpad rounds out the list of the ten most popular apps on the store as the third non-Google service to make the list after TweetDeck and NY Times, with about 35,000 weekly installs (almost a third of TweetDeck’s install numbers).

Obviously, it’s far too soon to draw any conclusions, but it’s certainly a testament to TweetDeck’s huge popularity to see it leading the most popular Chrome apps list, considering the company is primarily regarded as a desktop and mobile client software developer.

For your information, rivals HootSuite (16,000 weekly installs), eBuddy Web Messenger (13,9200 weekly installs) and Seesmic (5,442 weekly installs) are trailing far behind.