Shares climbed 1.6% on Tuesday as part of a broader tech rally, suggesting the market isn't worried about a looming Justice Department filing.

Now, Alphabet, Google’s parent company, may be forced to sell Chrome. The browser, which was launched in 2008 and integrates with Google’s search engine, is used today by some 3.4 billion people worldwide.

U.S. officials are recommending that Google sell Chrome following a historic ruling that the company has maintained an illegal monopoly.