Chickens require a number of essential aminos that are only found in animal derived proteins, they are after all omnivores not vegetarians. If you are using commercial feeds they will include (usually synthetic) methionine which is essential for good health and behaviour. Without it chickens will have poor muscle development, reduced egg production and will exhibit bad behaviours such as flightiness, aggression and feather pecking.
Methionine is present in meat (including offals), egg yolks, fish and some seeds such as sesame. For the average 'back yard' flock the best way to ensure sufficient in their diet is to include some of the above foods, or produce earthworms for supplementation to their diet.