LyonPride: I hope your chat with your neighbor is the solution, but I am sure the fence won't hurt.
I have a similar problem, but with my own dogs, a lab and a lab mix. We just moved to a rural property from the suburbs where they were leash-walked. They have had free run of our 20 acres for the past couple of years, and then, just last year, we got the chickens. My husband insists they need to be free range, but I know the dogs will eat them if they get a chance. Lucky for me they are older and slowing down.
cetrarchid's comment seems to suggest that you can break the dogs of this "habit". In my case, it is not actually a habit, but how do you train an older dog that was not raised around chickens to respect them?
Multiple methods may work. For me it involves maintaing exposure between problem dog and a chicken under controlled conditions. Controlled as in chicken behind a partition that dog can otherwise see, hear and smell chicken through. Keep dog near partition and reprimand dog every time improper activity is directed at chicken. More details but no time for here. Even dogs with established history can be broken of habit. Speed also a function of how you are in controlling dog.