Possums will eat eggs and will kill and eat your chickens. I free range mine and had the same experience you did. When I went to lock them up one evening, I found one in the coop. I never enjoy killing anything but I took on a responsibility to protect my chickens when I started keeping them. Even if you don't like doing it, sometimes you have to do what you have to do.
Since it was a young one, there is certainly a Mama and probably other siblings around somewhere. It may have recently been weaned and was looking for its own territory, or it may have already settled there. Possums are territorial in that they hunt the same area, and they will gang up and kill any new possum that moves into their area. But they get used to certain other possums in the same territory. They are not opposed to sharing their territory, just not with strangers. I've known towns and communities like that.
I suggest you get a trap and keep it set for a while. You can use almost anything for bait since they are scavengers, anything from bread to marshmallows to smelly meat to peanut butter, but you are liable to catch something else too. Could be a skunk or a raccoon, maybe a cat. You can talk to animal control to see what your legal options are. In many places, it is illegal to trap and release anywhere other than on your own property. Animal control may be practically useless or they might have a trap you can use and may dispose of them for you. You never know until you ask.
You are never going to totally get rid of them by trapping. There will always be others that can move into that hunting territory. But what trapping will do is remove any that are already hunting that territory. Sometimes you can go a long time before a new one finds your place.
Good luck!