I have not tried the chicken around the neck, though I did chase one dog with a dead chicken, didn't work.
I have three dogs two of them wolves, all three were killing my neighbors chickens if they got in our yard. Even though the chickens crossed into our yard I felt terrible, this has been over a year ago. All three of my dogs do not attack our parrots that we have had for years, for some reason they just know better. So I started raising my own ducks and chickens to train them to leave the chickens alone. Two of the dogs this worked with little effort and quickly within 2 months. One was stubborn and became a house dog during the day and released of a night to patrol the yard. Well the last couple weeks I have noticed that the one trouble dog while walking on the leash was no longer lunging for the chickens, so I started walking him through the chickens within nose length with still no response. For the last couple days I have tied him up with about 15ft of chain for a hour at a time and left him alone. I watched from a window as chickens walked around him to investigate as they usually do. Not once did he lunge or make a attempt to attack and one laid down in the dirt beside him to dust bathe.
Dogs are intelligent it takes time to break bad habits, but they do understand they are part of a social order. Once they understand the chickens are part of this order or family they can be broken. If a 10 year old wolf can be broke from killing chickens most dogs should but it takes time.