Sounds like a raccoon. I have had that happen, and tracked the varmint home. He/she (probably she) had a nest of kits in a hollow tree.
Raccoons usually kill by chewing the head, eating some, and leaving the rest. However, my experience tells me that when they have kits to feed, they take the kill home. Whether this is too early in the year for them to have young, I don"t know.
I have had coyotes come in small packs and stalk up and down my chicken yard fence, which is about 5". I have never had one come over. I would think it would be hard to carry a full grown chicken back over the fence.
But that doesn"t say it can"t happen.
In my experience, raccoons are the worst of the chicken predators. I don"t have much use for a raccoon.
A couple of nights ago I went out to close up my chicken house, and when I started back to the house, I looked and there was a big raccoon in my vacant dog house, just looking at me like I wasn"t there.
After due deliberation, I went back to the house and got my rife. Yep, he was still there. He is still there. I can"t imagine what happened to him. But the crows are grateful. I have to get around to putting him out in the field.