Old English cicen "young fowl," which in Middle English came to mean "young chicken," then any chicken, from West Germanic *kiukinam (cf. Middle Dutch kiekijen, Dutch kieken, Old Norse kjuklingr, Swedish kyckling, German Küken "chicken"), from root *keuk- (echoic of the bird's sound and possibly also the root of cock (n.1)) + diminutive suffixes.
Adjective sense of "cowardly" is at least as old as 14c. (cf. hen-herte "a chicken-hearted person," mid-15c.). As the name of a game of danger to test courage, it is first recorded 1953. Chicken feed "paltry sum of money" is by 1897, American English slang; literal use (it is made from the from lowest quality of grain) by 1834. Chicken lobster "young lobster," is from c.1960s, American English, apparently from chicken in its sense of "young."