Star's killed a several possums too. Little and big. Yes, they're good climbers. As mentioned, they are nocturnal, but I don't know how you would stop a dog whose intent on getting one. When we first moved in, both my dogs dashed to the edge of the woods and began digging furiously at a compost pile - then Star drug out a HUGE possum and started shaking it by the back of the neck - ugh- it pooped all over her and then went limp. (She was the center of attention at the dogpark that night! They ALL wanted to smell her! ) I went to move the body the next morning, but guess what? It must have been playing possum cause it was nowhere around--haven't seen it since- LOL!