Sounds like a fox but definitely a land based predator. I've never seen or heard of a hawk/owl/ airborne threat killing multiple chickens at once. This time of year, female foxes will bring food back to their den for their young pups as she is trying to wean them off her milk.
As mentioned above, if you leave the dead ones out, you'll maybe see what comes back for them, but they will also draw out other scavenger that may not kill a chicken, but would eat one already dead. Game cameras are a good way to see what is lurking/stalking around the coop, especially at night. Not sure what region you live in but pretty much the whole US has at a minimum foxes, raccoons, skunks, and opossums. The foxes and coyotes are more prone to attack during the day as well as at night. The others I mentioned are more strictly nocturnal.
Fencing in your chickens is for their protection since they are nowhere near the top of the food chain. Most people fence in an area around the coop so the birds can come out of the coop and have access to a protected area. From there, you can let them out to roam more of your property if you will be outside as human activity will usually deter most predators from getting close.
There's a ton of info on here about what to use to build an effective fence and how to construct it to keep out predators. The first step is to know what it is you are trying to keep out.
I have an area fenced in next to the coop that is about 20ft x 35ft. The fence is 8ft high and has netting over the top. The height gives me room to stand up when I go in and the birds have perches that stick out from the posts that they fly up onto during the day. The netting is because Hawks had dropped in like they are the 101st Airborne Division and my coop area is Normandy. I use welded wire for fencing and overlap it with chicken wire around the bottom part. This is to keep out smaller animals that could fit between the squares on the welded wire fence but its more to keep baby chicks in. The bottom of the fence should extend out like the bottom of the letter L. It can go along the ground or just under the ground but it should extend out 2 to 3 feet away from the chicken area. A determined fox, dog or coyote will try to dig under a vertical fence. Digging down and hitting fence that is horizontal will stop them from digging under to the other side. They naturally get as close as they can to their target then dig. Once they hit fence and can't dig, they may move laterally along the fence and try another spot, but they will not back up several feet and try to dig from further back.
This isn't the end-all of fences and fence options. I plan to incorporate electrical fence next month for my new fence area for my new flock of meat birds, but the fence I described above has kept losses to my laying hens to a minimum over the last 4+ years. Those losses were all white leghorns and they got killed while outside of the fence. Lesson learned there, nothing in nature is pure white. Those chickens were much easier to see and made very easy targets.