A chicken lived without a head for 18 months.
Chicken brains are concentrated at the back of the skull, and there isn't much to begin with anyway. For that reason, a decapitated chicken can survive for quite a while, living off just its nerve endings.
Mike the Headless Chicken is perhaps the most famous example. Its owner, a farmer named Lloyd Olsen, chopped his head off in 1945, but the chicken just didn't die. So the family kept him around and dropped food and water directly into his esophagus. It finally gave out after 18 months and considerable media attention.