If you're asking why, chicken has been used to suggest cowardliness since the 1600s here in Britain. Chickens are by nature very timorous creatures and easily frightened and, of course, 'way back then, they lived far more closely with humans than they do nowadays. Accordingly, they were an ideal choice for describing fearfulness.
The meaning tended to die out over the centuries until it was revived among the American military in the 1940s.