It could be a number of things from eye infection to clogged ducts to allergies. Sometimes, a dog is simply genetically predisposed to tearing. My eskimo dog, Yuki, has had tearing problems since he was 2 years old and he falls into the last category. His eyes are just watery and probably always will be.
One thing that did help him a little bit, though, was taking him off of grains. I switched him over to a grain-free food and his tearing is about half as bad as it used to be. Each dog is different, though, so I would recommend you take Chewie to the Vet and see if he or she can figure out what the problem might be.