The phrase "chaw on" means to chew or gnaw on something, typically something tough or chewy. An antonym for "chaw on" would be to swallow something quickly or without much chewing. Another antonym could be to nibble or take small bites of something delicately, as opposed to aggressively chomping down on it. Additionally, "spit out" could also be an antonym as it refers to rejecting something instead of consuming it. Overall, there are many antonyms for "chaw on" that relate to the different ways in which people consume and interact with their food.