This isn't a straight forward yes or no. If a puppy is socialised with chickens regularly when very young (before 12 weeks of age but ideally before 8 weeks) it will regard them as family later on in life and will not harm them. For an older dog, it varies between dogs and their breed characteristics. Some dogs are more ‘programmed' genetically to hunt and get a massive reward out of chasing and killing a chicken. Once a dog has done this once (or chased and caught wildlife whilst out on a walk) it is very hard to stop because the dog's brain (chemically) has had a massive reward from this behaviour. Yes, it is possible for a dog to be re-trained to avoid chickens but it takes an incredible amount of dedication, time and commitment to do this. Even after re-training, the dog normally only understands ‘safe and dangerous' - so when you are around it is ‘dangerous' and will not touch the chicken but if you were not in the garden at the time it becomes ‘safe' and will take the chicken.
Keeping Chickens