Well, if you were asking ME I would say you don't kill it. I would say you take the responsibility to secure your coop. Opossums are nocturnal and should not have access to your coop at night. However, that is simply not the popular opinion most of the time and I am sure there will be helpful killing tips soon. Opossums are quite sweet little animals and would rather have a nice bowl of cat food anyway if it is where they can get to it.
Nasty little critters, possums. Egg-suckers, and vectors for nasty diseases, such as EPM, which kills horses. Live trap? .22 rifle? A good dog? If you are sure your pets are secure, a bowl of dry cat- or dogfood laced with old-fashioned ethelyne glycol antifreeze might work, too.
Anytime the chickens are completely free range, then they'll suffer from predators. You may want to think about building a coop for the chickens to roost during the night. The chickens may not go along with the idea very well, if they've been used to roosting in trees for some time now. But the new hatching chicks can easily be taught to do so.
To trap an opossum, I would purchase an appropriate trap (sometimes you can rent them) and bait it with cat food or something else that has a strong odor. When the animal is caught, shoot it quickly. You could also wait for it to come again, as it probably will, and shoot it then. You'll have to figure this out for yourself.
Whatever you decide to do, kill it humanely.
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Any way you can. Gun would be my 1st choice. If you don't have one or are in a place where you can not shoot one, a baseball bat, garden spade--anything works.