We have rats. How do we get rid of the rats?

Ok, so here is the scenario... We have a chicken coop. And beside of this chicken coop is a really, really big field. Well, apparently rats lived in the field and they decided that our chicken coop was a much better home. So now there are DOZENS if not HUNDREDS of rats that swarm out at night and eat the chicken...stuff....We need the rats gone WITHOUT hurting the chickens. And with out leaving a bunch of carcasses laying all over the place for our dogs to eat...and get random diseases and die....Can anyone help us? It's really gross and I just do not do rats....I can deal with many rodents but NOT rats....