c. 1300, chacen "to hunt; to cause to go away; put to flight," from Old French chacier "to hunt, ride swiftly, strive for" (12c., Modern French chasser), from Vulgar Latin *captiare "try to seize, chase" (source of Italian cacciare, Catalan casar, Spanish cazar, Portuguese caçar "to chase, hunt"), from Latin captare "to take, hold," frequentative of capere "to take, hold," from PIE root *kap- "to grasp." The Old French word is a variant of cacier, cachier, making chase a doublet of catch (v.).
Meaning "run after" for any purpose developed mid-14c. Related: Chased; chasing. Ancient European words for "pursue" often also cover "persecute" (Greek dioko, Old English ehtan), and in Middle English chase also meant "to persecute." Many modern ones often derive from words used primarily for the hunting of animals.