We have two goats in our chicken pasture. They are actually quite fond of the hens, and seem to provide hawk protection--we haven't lost a bird to a hawk since we got the goats, and usually we lose at least two or three every fall/winter.
We introduced one goat as a kid, and the other as a full grown animal. Didnt' make a bit of difference. They were all nervous around each other for about five minutes. Now they all jostle together trying to get to scratch that I throw.
The goats do like to play "chicken bowling" where they will run up to and scatter a group of hens in all directions. I think they just like to see the hens scatter. The hens don't seem to mind--they scatter, then go right back to what they were doing.
I did have to re-do my chicken pop door. It was 12" x 14", and the goats could get inside the hen house and eat the chicken feed.
Oh, I almost forgot. Our goats are a Nubian doe and a Pygmy wether.