I'll bet you money that it's a raccoon. You can call the animal shelter and ask them to put a live trap out in your yard to try and catch it. It doesn't cost anything and it might work...raccoons are tricky buggers. They will reach through and pull the hens right up to the fence and behead them or eat them while they sleep (chickens are heavy sleepers).

Good luck, sugar. I'd love to loan you a goat (we have a very mini male right now that would work great), but I doubt that would go over well with the neighbors. It's a pity because goats are great at deterring predators in the chicken pen.