Will animals die if they eat a mouse who has been poisoned?

I have pet chickens out in my barn, but they are getting overrun by mice. We have considered putting out HAVOC to kill the mice, but we're afraid that my chickens will eat the mice and die too. Then my mother heard from one of her friends that the poison will only kill the mice, and not the chickens. Does anybody know if that is true, or will it kill my chickens? If it would kill the chickens, what should I do to get rid of the mice?