Chicken are prey animals in the Survivor Timeline.
The are very timid and run away when Lara gets near them.
Tomb Raider
In Tomb Raider, chickens can be found in the mountain village and shanty town.
Killing them provides XP, and with the Bone Collector Skill a small amount of Salvage.
Chickens along with rabbits must be killed and looted to unlock the "Tastes Like Chicken" Trophy/Achievement.
Rise of the Tomb Raider
In Rise of the Tomb Raider, chickens can be found throughout the Remnant village in the Geothermal valley. They provide feathers Lara can use to craft arrows.
Chickens are associated with one Trophy/Achievement, "Rotisserie", where Lara has to shoot a chicken out of the air with a fire arrow. There is also a challenge, "Fowl Play", in Geothermal Valley, to catch 5 chickens and throw them into the pen.