Where there's one there's lot's more, so you have a couple of choices.
1: Change the way you feed. Use a concrete slab, or build a wooden "eating platform" where there's a flat area of wood, with short sides framing it. Measure out what each bird gets, throw it onto the platform, let them have at it. Watching to make sure everyone gets some. They eat fast this way (think of cinderella when she feeds the chickens and the mice have to be quick to get some corn). No left overs for any other creatures, 2-3 times a day. My chickens were free range and had foraging options, so I don't know what sort of schedual cooped birds would have to be on.
2: Poison them, in a way that's chicken-proof so that they don't get into it.
3: Snake proof your coop, by placing screen over windows, setting the door higher off the ground if possible, removing the ramp if you have one, since chickes do have wings and are capable of flying short distances. Mine was 4 ft off the ground and never had a snake issue, even though we had a 6ft Rat snake living near.
Now, if you have rat snakes native to your area, be sure you have a snake friendly environment. Maybe you'll need to add a decent sized brush pile, or a rock pile with a cave like entrance, or design the coop floor to where the snake can live harmlessly below it without having access to the chickens. The presense of a snake will cause all rodents to vacate the immediate area. They can smell them, it's instinct. Once our female rat snake took up residence under the house through a crack over the basement door, I stopped finding rodent holes in my feed bags. The coop was about 10 feet from her "entrance" to her hideout.
I caught her smaller boyfriend and took him to the farm I boarded my horse at, and put him below the feed room. Stopped the mice there too. No more mouse nests in buckets! He wasn't happy about being moved, was what I would call aggressive.
But they're a harmless snake to people... would rather flee than encounter a human, not poisonous. Can't eat a grown chicken. I would leave extra eggs out where she could get them, once it became apparent the rodents were gone. I wanted her to stay on duty!
We still see her sometimes even though we haven't had chickens here in some 9 years. She must be old as dirt, she was big when she showed up! But under the house is warm for her in the winter, and there's no end to the small wildlife. Not to mention we haven't had a mouse problem indoors in forever either, even though it's a 130 year old decrepid house. LOL
Personally I hate snakes... never "liked" them, but I can't deny their effectiveness. I've only seen her a handful of times, my dad stepped on her once in the dark on the front porch. She just slid away, didn't coil up to bite or anything.
If by chance you like the "all natural" snake idea, you can call around to pest control places and request they drop one off for you. It has to be a Black Rat snake though. Gardner snakes and little things eat bugs and tadpoles and things not chicken related. You want a non-poisoness rodent catcher.
