In the past I had chickens and A goat (I wouldn't recommend getting just one goat, which it doesn't sound like you're doing). He was a pygmy and he did fine with the chickens. It was very common for me to find him sunning with the birds, with one or 2 laying right on him.
The biggest issue was keeping him out of the chicken feed. I accomplished that by putting a chicken sized pop door on the coop that he couldn't fit through.
I'm getting goats again myself, but intend to pasture them this time. I have a free range flock of bachelors that go into that field and I don't expect any problems.
My goat herd has done fine with the chickens cruising around their pen. I would not try to house the chickens with the goats because the goats will get into everything. Free ranging chicken in their pen is no problem though.
Your goats and chickens will be fine as long as they are not cooped up in the same house. Goats are smart, Houdini in many ways. You want to make certain they cannot get to the chickens feed. They will get down on knees to crawl through an opening. If they have horns, they could get themselves stuck.