I bought a covered litter box especially for the chickens. The hens love it and use it more than any of their other nestboxes.
ETA: Egg cartons can be purchased from eggcartons.com or do what I did. Ask friends and co-workers to save theirs for you. I'm overloaded with cartons now.
I had 2 of the large size litter boxes but my cat got too big for them. [ended up using a very large rubbermaid tote for the litterbox] I wish I had read about using the litter boxes for nesting boxes before we built some.