The axe blow is the fastest method when you have to kill several chickens.

Alternatively, use a very sharp kitchen axe against a wooden plank. Place the chicken's neck between the axe and the plank and hammer the axe. This is the slow approach

Alternatively, use a long sharp blade to sever the neck the same way you would slice a cucumber, with a fast sliding cut.

EDIT: Cannibalism is more frequent when there is some malnutrition. Of course, sometimes you have to sacrifice the worst offenders.