Joke aside, the Greeks were amazing storytellers but lazy in their monster design. 95% of monsters were just "random animal pieces paired together". So yes, an equus-gallus combination is probably in there. Multiple times.
@stavvers That's not that coincidental. Before the discovery of infectious agents like bacteria and viruses, the best hypothesis for disease that people could come up with was imbalances in the body's internal equilibrium. We just now have _slightly_ better empirical evidence for the substances in question.