Technically possible? Yes. Ideal for anyone involved? No. From the human's standpoint, chickens are extremely dusty (mine shake off literal dust clouds) and poop a lot. From the chicken's standpoint, they are much happier outside where they can better engage in natural behaviors. A dog crate is really only good as temporary housing and 4 hours outside of it is not going to be nearly enough free time. Chickens can be great pets, they're just generally bad house pets, they need more room and stimulation than many can provide indoors. I would consider other birds if you want a bird as a house pet, it's not that chickens can't be kept as house pets, it's just not what's best for everyone involved