My wife has chickens and we had two dogs that since have passed.
The first was a primitive mixed breed name Katie and the second was an Entlebucher Mountain dog named Karli (Entlebuchers are one of the 4 Swiss Mountain dogs, and the smallest at 45-65lbs and are used as a farm dog to herd cattle). Katie was the chicken killer, but she was not typical. She killed not for sport, but to have a chicken dinner. She would get one chicken, usually a neighbor's when she got out, take it into the woods, pluck it and eat what she wanted and we assume that she would bury the rest. Then she would clean up her face and paws. No evidence was left for anyone to find.
Karli did chase a chicken once when Katie went after and caught one of ours. But mommy broke a stick on a concrete pad, and she got the message that mommy was not happy and she wanted to make mommy happy (a typical trait from what I understand of the breed). Never went after a chicken again, and may have kept Katie from them also, but we have no evidence of that.
What we know that did break her from going after our chickens, but not necessarily the neighbor's, were 5 Silky Roosters that we ended up with for a while. They did not run but instead stood up to her and she got the message. Mommy's chickens were not worth the effort, if she wanted a chicken dinner she had to get out the fence (chain link fence with an e-fence along the bottom to stop jumping over) and go next door.
My wife is the dog training expert (not really, but is compared to me), and she could go into pages on how to use clicker training, treats, and other positive measures that would help with this. She did some of it with Katie, but she has medical issues that kept her from working with the dog as much as was needed or that she wanted.