Yes. This is a very real phenomenon. All chicken flocks have a well-defined pecking order. It's their way of preventing mayhem.

The lucky chicken at the top of the pecking order basically gets to push everyone around. She gets first access to food, water, prime roosting spots and so on. If she doesn't like what anyone else is doing she has full pecking rights. She gets to tell any other chicken to bug off. The poor baby at the bottom of the pecking order is in the exact opposite situation: everyone in the flock can peck her, and she has last rights to food and other resources. The other chickens in a flock fall somewhere between these two extremes. The #2 chicken can only be bullied by the #1 chicken and can bully everyone else in turn, and so on and so on.

Pecking order is established at a very early age and usually remains unchallenged until death.