Mike the Headless Chicken is a classic story!
As for "hypnotizing chickens," I'll go brainy geek on y'all.
What's happening when you "Hypnotize" or "trance" a chicken by holding them upside down or drawing lines in front of their faces is what's actually known as "Tonic Immobility." It's a unique adaptation that Mother Nature has given chickens, as well as many other animals such as pigeons, rabbits, mice, opossums, sharks, snakes, and many other animals as an escape mechanism. By becoming immobile, the prey animal is able to fool a predator into thinking it's died. Without movement to stimulate it's drive, the predator will either lose track of it or lose interest and leave.
Interestingly, by studying the brains of chickens in tonic immobility, it's discovered that they are not really hypnotized. All of their brain functions are fully wide awake and aware. However, they have been found to have a large influx of serotonin to the brain, which is a neurotransmitter that does a variety of things, but most notably, affects anxiety and mood. So perhaps it also allows the chicken a bit of mercy from the fear and stress of impending death.