Apple seeds contain cyanide in small amounts, i know it will kill my parrots but im not sure about chickens, i wouldnt give it to them just to be on the safe side.
True parrots shouldn't eat them. I give my chickens whole apples or cut in half, with no ill effect. Chickens don't break open the seeds like parrots do. But I don't think I would put just cores in there just to be safe.
There was another thread talking about feeding apples to chickens... It prob'ly takes a lot of seeds to kill a chicken, but I wouldn't take the chance.