Yes, chickens can eat both the rye plant and grain head. Keep the amount provided to less than 10% of the hens' diets or you may see production losses from the dilution of nutrients (namely protein) in the diet and possible reactions to anti-nutritive substances naturally found in the grain. If they are not mature birds, feeding it as more than 10% of the diet for an extended period of more than a week or two may cause vitamin or trace mineral deficiencies and/or may delay the onset of lay.