My cat kills lizards, mice, baby rabbits... and turns a blind eye to our chickens. Just ONCE I told her 'Jade, MINE!' and she stopped, licked her tail for a few moments as if she had never THOUGHT of a chicken dinner, and never harassed them seriously again. The doves that steal chicken food, however, are fair game and she'll bring down a couple a day.
Before the coyote killed our flock she would occassionally playfully run at certain chickens to get them to yell at her. Our Barred Rock hen would chase her for it and they all seemed to enjoy it. She used to tease our goose too, but it wasn't hunting behavior at all...