mid-13c., chace, "a hunt, a pursuit (of a wild animal) for the purpose of capturing and killing," from Old French chace "a hunt, a chase; hunting ground" (12c.), from chacier (see chase (v.)).
The meaning "a pursuit" (of an enemy, etc.) is from early 14c. The sense of "occupation or pastime of hunting wild animals" is from early 14c.; the meaning "group of hunters pursuing game" is from 1811. The sense of "piece of privately owned open ground preserved for animals to be hunted" is from mid-15c.
"groove cut into any object," 1610s, from French chas "enclosure, enclosed space," from Vulgar Latin *capsum, from Latin capere "to take, receive, contain" (from PIE root *kap- "to grasp"). The meaning "bore of a gun barrel" is from 1640s.
Old English æfter "behind; later in time" (adv.); "behind in place; later than in time; in pursuit, following with intent to overtake" (prep.), from of "off" (see off (adv.)) + -ter, a comparative suffix; thus the original meaning was "more away, farther off." Compare Old Norse eptir "after," Old Frisian efter, Dutch achter, Old High German aftar, Gothic aftra "behind;" also see aft. Cognate with Greek apotero "farther off," Old Persian apataram "further."
From c. 1300 as "in imitation of." As a conjunction, "subsequent to the time that," from late Old English. After hours "hours after regular working hours" is from 1814. Afterwit "wisdom that comes too late" is attested from c. 1500 but seems to have fallen from use. After you as an expression in yielding precedence is recorded by 1650.
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.).
The meaning "run after" for any purpose is by 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 "chase" words often derive from verbs used primarily for the hunting of animals.
"pursuit of anything in ignorance of the direction it will take," hence "a foolish enterprise," 1592, first attested in "Romeo and Juliet," where it evidently is a figurative use of an earlier (but unrecorded) literal sense in reference to a kind of follow-the-leader steeplechase, perhaps from one of the "crazy, silly" senses in goose (n.). Wild goose (as opposed to a domesticated one) is attested in late Old English (wilde gos).
mobile foot-soldier, 1796, French, literally "huntsman," from Old French chaceor "huntsman, hunter," from chacier "to chase" (see chase (v.)).