"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).
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.)). Meaning "a pursuit" (of an enemy, etc.) is early 14c. Meaning "occupation or passtime of hunting wild animals" is from early 14c.; meaning "group of hunters pursuing game" is from 1811. 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"). Meaning "bore of a gun barrel" is from 1640s.
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.
"a large waterfowl proverbially noted, I know not why, for foolishness" [Johnson], Old English gos "a goose," from Proto-Germanic *gans- "goose" (source also of Old Frisian gos, Old Norse gas, Old High German gans, German Gans "goose"), from PIE *ghans- (source also of Sanskrit hamsah (masc.), hansi (fem.), "goose, swan;" Greek khen; Latin anser; Polish gęś "goose;" Lithuanian žąsis "goose;" Old Irish geiss "swan"), probably imitative of its honking.
Geese are technically distinguished from swans and from ducks by the combination of feathered lores, reticulate tarsi, stout bill high at the base, and simple hind toe. [Century Dictionary]
Spanish ganso "goose" is from a Germanic source. Loss of "n" sound before "s" is normal in English (compare tooth). Plural form geese is an example of i-mutation. Meaning "simpleton, silly or foolish person" is from early 15c. To cook (one's) goose is attested by 1845, of unknown origin; attempts to connect it to Swedish history and Greek fables are unconvincing. Goose-egg "zero" is attested by 1866 in baseball slang, from being large and round. The goose that lays golden eggs (15c.) is from Aesop.
Old English wilde "in the natural state, uncultivated, untamed, undomesticated, uncontrolled," from Proto-Germanic *wildia- (source also of Old Saxon wildi, Old Norse villr, Old Frisian wilde, Dutch wild, Old High German wildi, German wild, Gothic wilþeis "wild," German Wild (n.) "game"), of uncertain origin, perhaps from PIE root *welt- "woodlands; wild" (see wold).
Ursula ... hath bin at all the Salsbury rasis, dancing like wild with Mr Clarks. [letter, 1674]
Meaning "sexually dissolute, loose" is attested from mid-13c. Meaning "distracted with excitement or emotion, crazy" is from 1590s. U.S. slang sense of "exciting, excellent" is recorded from 1955. As an adverb from 1540s. Baseball wild pitch is recorded from 1867. Wildest dreams attested from 1717. Wild West in a U.S. context recorded by 1826. Wild Turkey brand of whiskey (Austin Nichols Co.) in use from 1942.