If it was during the daytime I would suspect a hawk. They only eat the heads (brains) and leave the rest. If evening then you might be right about the opossum. Or a raccoon. Last fall I had hawks attacking by day and raccoons by night. Lost 7 total chickens and we locked them up for rest of winter.
If it was a hawk there would be a huge pile of feathers. If they had time to eat, there won't be much left to the carcass. If they get scared away, the dead bird may be a good distance away from the feather pile.
I have not had personal experience with any other predators but have heard that raccoons will take head if that's all they can grab from outside the pen. If they get inside they will often kill multiple birds and take just the contents of the crop.