Do I get any benefits from petting my chicken?

Petting your livestock (basically interacting with it like you would with a villager) increases its happiness. As your livestock becomes happier (visible by the info screen that comes up after you try to interact with it a second time), it has a higher chance of producing better versions of their normal produce, such as Large Milk, Large Egg, or Large Goat's Milk.

Basically the Chicken looks forward to being petted by you. When it does gets touched it gets happier and is more encouraged to produce better quality food.

A thing not mentioned in other answers: When you pet your chicken inside a barn/coop, you also gain 5 experience points towards the Farming skill.

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