If you caught a possum in there once, rest assured its probalby still around...they don't travel much once they have a home. Can't believe you had it and let it go! It won't stop with stealing eggs, which is bad enough. It will eventually kill a chicken.
The way i learned to 'dispatch' a chicken, how all the old folks I knew did it, is quick and I think less traumatic to the chicken that restraining it and stretching its neck out across something so as to chop it with a hatchet or something, and I never could figure out how I'm supposed to hold the body with one hand and the head I was trying to stretch out with the other and then locate my third hand to wield the hatchet ...plus I was always afraid I'd miss and chop my own hand or something...
Hold the chicken in your arms, take hold of both feet/ankles firmly, gently 'roll' it's body forward, and upside down so it's hanging from your hand holding the legs...doing it in a slow roll keeps it calm. Chickens really relax if held and carried upside down by the feet like that. Hold the bird along your side, stoop slightly so the bird's head is at the ground, the bird will have neck bent upward so as to hold head parallel to the ground. Lower it enough you can gently place the arch of your foot, on the same side of your body as you are holding its feet, across the neck just behind the head. Press down firmly enough to hold the neck down, with the head 'stopping' at the inner edge of your shoe sole, and while holding, straighten your body and lift the bird by the legs in a quick, firm but smooth motion. Don't jerk, and don't pause, do a solid follow through on your lift, and the head will detach quickly and easily. Job is done.
Another way is to use a 'killing cone'. One of those orange road cones works. Open the small end big enough to slip a chicken head through. Attach it something to hang small end down. Lower the chicken into it head first, holding the legs. Slip the head through the hole and the bird will rest that way as you then cut the head off. I've seen people use pruning loppers to remove the head.
Both ways, quick removal of the head kills instantly.