"body of soldiers who are dropped by parachute into enemy territory," 1940, from parachute + plural of troop (n.).
Entries linking to paratroops
parachute n.
"apparatus, usually in the shape of a very large umbrella, carried in an aircraft, that may allow a person or thing to drop to the surface below without injury or damage," 1784 (the year the first use of one was attempted, in Paris), from French parachute, literally "that which protects against a fall," hybrid coined by French aeronaut François Blanchard (1753-1809) from para- "defense against" (see para- (2)) + chute "a fall" (see chute).
PARACHUTE, a kind of large and strong umbrella, contrived to break a person's fall from an airballoon, should any accident happen to the balloon at a high elevation. ["Supplement to the Encyclopaedia or Dictionary of Arts and Sciences," Philadelphia, 1803]
troop n.
1540s, "body of soldiers," 1540s, from French troupe, from Old French trope "band of people, company, troop, crowd" (13c.), a word of uncertain origin, perhaps from Frankish *throp "assembly, gathering of people" or another Germanic source, perhaps related to Old English ðorp, Old Norse thorp "village" (see thorp). OED derives the French word from Latin troppus "flock," which is of unknown origin but also might be from the proposed Germanic source. Of groups of animals from 1580s. Specifically as "a subdivision of a cavalry force" from 1580s; of Boy Scouts from 1908. Troops "armed forces" is from 1590s.