Dog Chasing and Killing Neighbors' Chickens
Chasing and killing chickens is predatory behavior. It's natural for many dogs and very rewarding for them, so it won't stop with training alone. Because predatory behavior comes with little or no warning, the first step is to make it impossible.
The most reliable answer is secure fencing he can't get over, under or through. Supervise him outside and keep him on a leash or long line near the neighbors' animals until the yard is secure. Being tied up for long periods isn't a good long-term answer and can add frustration.
Alongside that, work on a strong recall using high-value rewards. Start indoors and build up slowly to bigger distractions. A reward-based trainer or a veterinary behaviorist can help. Don't use shock collars, which carry welfare risks and work no better than reward training. Daily exercise and games like fetch or scent work give him a better outlet for the chase drive.
See dog aggression and biting and dog behavior problems.
This is general information, not a diagnosis. Please follow your own vet's advice.