You need a cat or dog that is young and vigorous, lives outside, and is kept on the hungry side. Not sure about dogs for this purpose but with cats it's best to have a kitten from an experienced mouser for a mother....the mother teaches the kittens to hunt. The kitten
should be at the age where the mom is not interested in being sociable with it before adoption......
Perhaps another solution would be to combine your compost with your chickens....just throw all the compostables to them direct. They will quickly eat most of what might interest the rats direct, and encourage the composting of the rest, while repelling other critters by means of their manure.