You gas the rats in the day time while the chickens are free ranging and while the rats are home. Propane. There is some youtube video's if you want to look it up. Some ignite it-----I wouldn't under the coop. Boom!
Some even hook hoses to their car exhaust.
Very carefully!!! LOL. I would!! I would find rat holes and stick/seal a hose in them attached to a tank and turn the tank on a few minutes then move to the next hole, etc.
I had rather smell a dead rat a few days than see him running around and in the chicken feed, coop, etc. I would gas them---if it was that bad----just have to make sure the Smokers were not lighting up. Boom!!
Chickmom, what are the rats eating----are your chickens wasting a lot of feed??? Rats that bad and many have to have food?? Remove the food(or their access to it) and the rats should go some where else to eat?? Live Trap them, go out at night and shoot some with a pellet gun, gotta get rid of them.
Sure "rats" "can" kill the chicks. Rat proof the coop and set traps for the rats if poison is not usable.
Have you tried this hen before to see is she will adopt chicks? Some do and some don't?