Hi, John Stuart -- Did you read the post above yours? "Your dog likes chew toys" is fine. "Chew toys" is a noun in this case, not a verb. "Your dog likes to chew toys" is also a correct sentence, but it means something different.
What kind of toys does the dog like? The dog likes chew toys.
What does the dog likes to chew? --or -- What does the dog like to do with toys?