Yep I too would say check with your dr. Our oldest did this and it was because his adnoids were so big he couldn't breathe through his nose properly so he never closed his mouth all the way.
I was going to suggest tonsils/adenoids too. DS had his taken out at 2 1/2. He had just stopped drooling a couple months before, but I think they were behind the drooling. (Took him until past 2 to learn to coordinate swallowing around them IMO.)