to hypnotize a chicken - place chicken on floor, strech legs out behind it and neck in front. place finger in front of beak and gradually move it away in a straight line. hold position for at least 10 seconds.
the chicken will stay motionless and quiet for a while. not long enough to take it from a car to your seat, but for a while. however, if after stretching it, you were to wrap in it a breathable dark fabric (somewhat loosely, but restrained enough that is stays stretched out), i would bet it would be, at the very least, extremely docile until removed from the cloth.
also, basically any bird is is pretty docile if you just cover their eyes.