The iPad version of Twitter, provides a preview of URLs within the app. An extension for Google Chrome brings this feature to the regular desktop version of twitter and also desktop notifications for new tweets.
Install Twitter Desktop Notification & Preview URLs and go to Twitter homepage.
Now, whenever you want to preview a URL in a tweet, select the tweet and in the right side panel of Twitter you will get a small preview of it as seen above. You can also get a fullscreen preview by pressing the “p” key. If there are multiple links in a tweet you can use the the arrow keys to navigate them.
The extension can also alert you when new tweets are received via Desktop Notifications.
To configure Twitter Desktop Notification & Preview URLs access the settings panel from the user menu on the top-right corner of Twitter.
Download: Twitter Desktop Notification & Preview URLs