You'll meet the first chicken when passing the Kata'el. Then you'll need to restore the Hennery, which is already in your camp near the Cowshed and Windmill.

 

Bird Feed can be made in the Windmill using Water and Corn. As soon as the feed is ready, it'll move to the Hennery. Drag the feed to the chicken in the Hennery, and you will get a basket of eggs.