It may be a mild case of conjunctivitus - i would go to the vet they will give you some drops for him , hes a cutie 
ther's a product called eye envy...Karbo said:My chihuahua has really bad stains under his eyes. He's brown and white, but around his eyes he's white so it's really noticable. Warm washcloths don't work. Is there any way to get rid of it?