I use live traps like the Victor, that has a small hole they enter and after they are in, they can't get out. It is just a rectangular box with a see-through window so I can easily see when there are mice in there, but there is no danger to the chickens. No poison - I bait it with peanut butter. When there is a mouse in the box, I take it some distance from the coop, with the birds following eagerly. I then open the box, the mouse or mice hop out, and the birds grab them, kill them and eat them. Occasionally one will get away and probably returns to the coop but most do not. It is an extra source of protein for the birds, and every one they eat, reduces the population by more than one if you count the subsequent generations and how fast they breed.
Mice tend to be most active at night, coming out to eat, which is why the birds don't kill many on their own. But if I catch them - they are more than happy to help get rid of them during the day.
