Chicken hypnosis is a form of tonic immobility-- the state wherein an animal that is put under certain stressors becomes temporarily semi-paralyzed in a form of catalepsy. While specific reasons as to why this happens are unknown, it is thought that the "hypnosis" might be due to thanatosis, a specific kind of tonic immobility wherein an animal under threat plays dead (as seen in possums). It is a fear response, though chickens who are immobile will have their heart and respiration rates, as well as their body temperature, lower.
There are a myriad of ways to hypnotize a chicken.
One of the most well known is probably the "line" method.
1. Take chicken.
2. Lay on its side, wings folded close, head resting on the ground.
3. From where its eyes are, draw a line in the dust (or with chalk) directly away from its face.
4. Repeat a few times.
5. Release hen.
As you might've gathered, the actual line bit isn't important. The important part is restraining the chicken in an awkward position to make them pass out in fear. It also works if you have them on their backs or, if you're like 10 year old me, put them on your head, upside down, and walk around holding them up like you're that girl from the end of Jungle Book who carried a water pot on her head.