Cassell’s Dictionary of Slang
CHOPS noun: 1) [18th century and still in use] The jaws, the mouth, the lips. 2) [1940s and still in use] (originally U.S. Black) Ability, skill, competence. [from jazz musicians figurative reference to the use of one’s mouth and lips in playing a wind instrument]
Based on this, it probably just got picked up and morphed to refer to talent in general.