OR... a possum.
I had a hen killed two days ago and her head was missing. The predator had to climb into the pen to get her (chain-link). I knew the little pest would be coming back for the rest of her, so I moved the extra-large trap right beside the pen, and put the rest of her carcass in the bait basket. The very next day, there was a possum in there. He was only a baby (she was only a bantam) but the other two chickens in that same pen haven't been touched since. The possum was relocated through Animal Control yesterday, and once I get the trap back I plan to reset it just in case.
But the fact that I caught a possum and the other two chickens in there haven't been touched, tells me that possum was probably the culprit. But the evidence is the same - missing head.