Wow your possums eat chickens?... In Australia they're only herbivores and the worst they do is move into your roof and bang around. I couldn't imagine worrying about skunks and what not. Though foxes are a problem here and my partner and I have put out some traps and the game camera though the foxes are smart and the only thing we caught was the neighbours cat who we promptly returned safe and sound... though a little cranky that he was stuck in a cage lol.Oh, I'm so sorry for your loss.... that really sucks, and it makes me so mad that these stupid predators cause us so much problems. I mean, I know they are just doing what comes naturally to them, but go do it somewhere else! haha
But I'd say definitely a trail camera, if you can! I have several of them (I use them mainly for deer season) but now have one pointed at my rooster coop. Here's a big possum I caught on camera a couple months ago.
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Here's a picture of a Aussie possum who used to visit my old flat years ago... he/she was very cute.