Etymology
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chase (n.1)

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.

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give (n.)

"capacity for yielding to pressure," 1868, from give (v.). The Middle English noun yeve, meant "that which is given or offered; a contribution of money," often as tribute, or in expectation of something in return.

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chase (n.2)

"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.

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give (v.)

Old English giefan (West Saxon) "to give, bestow, deliver to another; allot, grant; commit, devote, entrust," class V strong verb (past tense geaf, past participle giefen), from Proto-Germanic *geban (source also of Old Frisian jeva, Middle Dutch gheven, Dutch geven, Old High German geban, German geben, Gothic giban), from PIE root *ghabh- "to give or receive." It became yiven in Middle English, but changed to guttural "g" by influence of Old Norse gefa "to give," Old Danish givæ.

Meaning "to yield to pressure" is from 1570s. Give in "yield" is from 1610s; give out is mid-14c. as "publish, announce;" meaning "run out, break down" is from 1520s. Give up "surrender, resign, quit" is mid-12c. To give (someone) a cold seems to reflect the old belief that one could be cured of disease by deliberately infecting others. What gives? "what is happening?" is attested from 1940. To not give a (some thing regarded as trivial and valueless) is from c. 1300 (early examples were a straw, a grass, a mite).

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chase (v.)

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.

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give-away (n.)

also giveaway, "act of giving away," 1872, from verbal phrase give away, c. 1400 (of brides from 1719); see give (v.) + away (adv.). The phrase in the meaning "to betray, expose, reveal" is from 1878, originally U.S. slang. Hence also Related: give-away (n.) "inadvertent betrayal or revelation" (1882).

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give-and-take (n.)

1769, originally in horse-racing, referring to races in which bigger horses were given more weight to carry, lighter ones less; from give (v.) + take (v.). General sense attested by 1778. Give and take had been paired in expressions involving mutual exchange from c. 1500. Give or take as an indication of approximation is from 1958.

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wild goose chase (n.)

"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).

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chasseur (n.)

mobile foot-soldier, 1796, French, literally "huntsman," from Old French chaceor "huntsman, hunter," from chacier "to chase" (see chase (v.)).

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dog-tired (n.)

"as tired as a dog after a long chase," 1806.

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