Yeah... You can train them out of that. It does take time and a lot of effort. However, having gone from "I have a husky who tries to slaughter my chickens enmasse. Oh help. What am I going to do. I don't want to get rid of her but she will NEVER change, she just stares at them desperately all day long with her mouth watering, crying, trying to bite them through the fences, not even a shock collar stops her..."
To "Oh. A chicken is out right next to the husky. Come here husky! Good dog not attacking the chicken. Stay. I'm going to put the chicken away now."
I know from experience that it can be done.

(She still kills other things, her newest love is hunting rats, but not the chickens. She ignores them.)
And if you have the option to cull them yourself, you should step up, take responsibility, and do so. It's the best thing for all the animals. Being responsible for the lives in your care is the most important thing about owning them. If you can't do it or find someone to do it in a humane way, you may want to rethink taking on that responsibility.
Accidents between chickens and predators happen. So do accidents between people and cars. That doesn't mean we should encourage them.
