The longest a chicken has survived without it's head was 18 months after a farmer cut off it's head.
The farmer who cut off the chickens head had a failed attempt at slaughter, axed off his head and missed the jugular vein which is required to kill the chicken.
So when you slaughter a chicken you must make sure you cut the Jugular vein before cutting the chickens head.
Usually just chopping off the chickens head should severe the Jugular Vein and kill the chicken but it's best to cut the Jugular vein to render the chicken unconscious before you do axe off the chickens head.
The chicken won't be able to eat or drink without it's head though so the chicken may die sooner without a head but that was amazing that the Mike the chicken lived 18 months without it's head before it died.