In such a case, you can do a couple of things and see what works best for fixing it. Start by restarting the computer and go back to Gmail to see if it opens now. If that doesn’t work and Gmail won’t open in chrome still, use a different browser to be sure that its chrome that has the problem. If that indeed is the problem, clear the cache and cookies from chrome and try again.
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Read all above Official Blog Post to Fix Gmail Account.

#gmail won’t open in chrome