Every time that my wife and I visit her family in Colombia we have sancocho de gallina (gallina=hen). Everybody keeps a chicken or two or three, generally with a string tied around one of their legs to keep them from getting away.
My wife can't bring herself to kill the chicken, so her mother usually does it. The method is to grab the chicken by the head and swing it around very fast in a circle, snapping the neck.
The last time, her mother had some difficulty swinging the chicken with enough force to do the job, and it took several tries. (I felt kinda' sorry for the chicken.)