From the Golden Books Guide to Field Identification: Birds of North America, Copyright 1983 by Western Publishing Company, Inc.:
Greater Roadrunner - Large, crested, terrestrial bird of arid Southwest. Wings are short and rounded. Runs rapidly, trailing its long, white-tipped tail. Seldom flies. Eats lizards, snakes, insects. Song, dove-like, each note lower pitched.
Sounds as if the roadrunner is more interested in your garden critters than in your chickens. Still, I'd put some deer netting or other protection over the coop. Perhaps there is a bird-watching society in the area who could give you more information about this particular bird and if it is a danger to your babies. Hope everything works out okay.