I'd get the rat with a live trap and not mess with poisons around my chickens. With the proper bait, a live trap is irresistible. Rats like peanut butter, grain, cheese, and sandwich meat.
My father in law has woodchucks and oppossums underneath his barn, which do terrible damage to his crops (and are chicken killers, too). He live traps them and puts the trap in a barrel of water so he doesn't have to shoot the trapped critter. He was a cop, so shooting an animal isn't a problem. It's just that ammunition's expensive.
Once you've eliminated the rat, try to fill in the drainage system if possible. Set a tiny, very smoky, contained fire in one of the entrances and let the smoke help you find all the openings, then plug them. Use big chunks of cement capped by fresh cement, or lots of rocks. Rats can squeeze through very tiny holes!
Your chickens might be ignoring the rat right now, but rats kill and eat chickens and eggs, and spread all manner of nasty diseases. Rats are nimble, clever, wary, and learn from their mistakes.
Here's two website about using live traps and what kinds of baits work best;
http://www.animalsheltering.org/resource_library/magazine_articles/jul_aug_1998/how_to_set_a_live_trap.html
http://www.pestproducts.com/animaltrapping.htm
If you really must use poisons, get something like D-Con blocks and set it far off the ground where your chickens won't get at it. Rats climb easily, so on top of the coop roof is ok. A rodent poison which contains coumadin (warfarin) is most effective. I'd also put some of the poison blocks in the drainage tunnels, far enough in so the chickens won't be able to find it.