Raccoons have been a problem killing poultry for me, so they get shot, or livetrapped and then shot. Skunks and possums have only eaten the eggs and never attacked the birds, so I let them live. If a possum moved in, as in, inside the barn and dining on eggs everyday, he got livetrapped and taken for a ride to a wilderness/wildlife area. I learned from a man named (of course) Skunky how to livetrap and release skunks without getting sprayed, so skunks who persisted coming inside got relocated too. This then led to an unintended "hobby" as the local go-to person for removing skunks!
Now for the mea culpa--livetrapping and relocating/releasing these animals isn't legal where I used to live and did this. All I can say is that a little governmental bird told me just not to get seen doing it. The rationale is that they might have rabies, and also that you might move your problem varmint to somebody else's farm to trouble them. You were allowed to kill them but not relocate them. Since the skunks and possums weren't hurting the poultry I decided they deserved a "pardon".
I did find one little possum in a nest box holding an egg and delicately lapping it up, having removed the top of the shell. When I stood over it looking in, it just looked up at me like "I'm sorry, did you want some?" A big one started climbing up on the box where I put my barn cat food, and I was in the habit of stroking the cat as I was on my way back to the house after evening chores. A couple of times I ended up stroking the possum!
Possums aren't real smart, the only way I know to make them go away is to trap and relocate or kill them. For me, with skunks and possums it was often live and let live. You might try closing up the opening it's using for getting in with your chickens; if it can't get any dinner it will eventually look elsewhere.