My experience has been that genetics play a significant part here. Training is invaluable, but very high level prey drive is not an extinguishable drive. One can build drive, bring it out, or keep from eliciting it. One can also teach an alternate behavior-- provided that the prey drive is not very high.
Here's Grimm, Czech Border Patrol lines, both sides. For the work, these dogs were bred to be extremely hard, intense, extreme, drivey, and have that combustible combination of hair-trigger excitability coupled with low frustration threshold. However, Grimm has low - medium prey drive for his type.
How did we teach Grimm to be comfortable with our free-ranging chickens? Two methods: Body Blocks (a method dogs naturally use regarding desired resources, imposing your body between the dog and what he's interested in, and projecting your energy forcefully towards the dog to say "Keep off-- This is Mine.") made known by behaviorist Patricia McConnell, and 2 small taps with an e-collar. I am neither in favor of e-collars nor against them. They are only a tool-- and the DOG determines which tools and methods he requires, not us and our ideals.
Grimm can now be free, offlead, in the yard with the chickens free-ranging. There is no chasing. Okay, all isn't perfect-- Grimm still tries to steal the chickens' snacks! Here, he's jonesing for their mixed salad greens!
So yes, train, using the methods and tools and techniques that your dog responds best to.
Remember the value of soothing, calming praise over exciting praise. Be consistant, and keep at it. But, be realistic as well, in that if the dog has high prey drive, and the chasing and killing part of the hunting sequence is strongly influencing your dog around critters that move, the dog may be unable to be reliable.
Here's wishing you every success!