If you've installed tweetdeck for chrome you can use this extension to open TweetDeck for chrome with a browser action.
When you don't use the chrome new tab (as your homepage), you can't use TweetDeck for chrome, because you can't open it. With this extension you can!
If you've installed TweetDeck for chrome you can use this extension to open it with a browser action. And if you've already opened TweetDeck in a tab, you can click the icon to return to that tab.
You can get TweetDeck for chrome here: https://chrome.google.com/webstore/detail/hbdpomandigafcibbmofojjchbcdagbl
Note that this not an official extension!
I hope you can give me feedback, if it doesn't work or something...