Goats are big time prone to coccidiosis (sp) so you run a big risk there and the other thing is that if the goat gets hold of some eggs that have been there for a few days that one of your girls has hidden somewhere it can kill her, at the very least make her incredibly ill. I would house them seperately.
My biggest concern would be the food, too. Goats will binge on just about anything. They may nibble on the chickens if they're docile, too. They don't do it to be mean. To them, if it tastes good, they're going to eat it.
We let our chickens free range with the goats, but they do have separate housing and feed areas. Maybe you could just section off an area that the chickens are able to get into to feed and lay, but the goats can't squeeze through.
Been raising goats with chickens for a while now - The chickens have access to the goat's food, but the goats do not to the chickens' food. If your chickens have diseases the goats can catch, you need to get rid of them.
Otherwise, healthy poultry and healthy ruminants can live quite well together.
That is exactly what I do. They free-range together but have separate housing. My chicken feeders are all in the tractors and house and I have each opening set-up to be too small for the goats to go in. I have NEVER had a problem with them getting to the chicken feed. Now the chickens get in the goat feed but usually the goats have eaten their amount I have fed them.
It may depend on the breed of goat but my goats NEVER NEVER have been aggressive to my chickens - never WANTED to nibble, even when they are bored. They are always just hanging around browsing or snoozing. They like when the chickens get on them and groom them - a massage. Lulls them right to sleep.