Tucker loves to chase small fuzzies. I don't know for sure that he'd kill them...he once stalked our momma rabbit (lives in the yard) who has become habituated to us. He was on his long lead and I wasn't going to let him get her. She just layed there and when he was like four feet away she just sort of hobbled off, started to run and then stopped short where she had been laying and ate her poop instead lol. But he has killed a mouse (and swallowed it whole) and when he is close to a wild animal and it takes off he does a banshee cry because he can't get it. So I think he would kill it, but I don't plan on letting it happen, I like the little fuzzies. I am afraid Tucker might have a hard time living with cats other than our two, he still chases ours but doesn't hurt them. The way he reacts to cats outside is very concerning though.