Whoa, what an inspirational chick!
I personally love domesticated rats, they're one of my favourite animals. I've owned 9 thus far but got too busy with school to keep up with stimulating them. They're a step below dogs, if you treat them right. All the same, I haven't hesitated to put out mouse and rat snap traps in our home and the chicken coop. It's no different than any other domestic or feral animal. You wouldn't hesitate to shoot or take action against a coyote or a violent feral dog; those aren't the same as your family mutt. Don't get em confused hehe.
 
As others have said, make sure you clean up that poison and their droppings real good before you let your chickens out. Having a hen eat that would be a nightmare.