Some breeds of dog can not be trained to never kill the chickens.
However, ALL breeds can be trained not to kill or chase them when you are there to supervise.
BUT, when you are out and the dog is alone with the chickens and something happens, like the chickens start fighting, or they start flapping about something, then the dog may well get triggered to kill them again.
Dogs that I would class in the 'untrustworthy' group (only once they have offended once before), are hunting dogs such as terriers, huskies, and greyhounds, whippets etc.