Firstly, it will make them unhappy. They prefer to be outside. Keeping a chicken inside your home permanently prevents them from expressing their natural behaviors. It is very important that chickens have several hours of free-ranging each day for their physical and psychological well-being. Chickens enjoy foraging in a yard for tasty snacks such as bugs and plants, which is not possible in your house. (At least, we certainly HOPE it's not possible for them to forage bugs and grass from your floors!) Instead, indoor pet chickens may eat bits of carpet or other detritus that is not good for them and could cause them serious health problems. And if you have your hen in a diaper, she will also be laying her eggs in the poopy diaper--yuck! Then she'll be toting the egg around in the little diaper pouch until you've noticed and relieved her. And if you don't have her in a diaper, then she'll be okay laying her egg, but your indoor pet chicken will be spreading her feces around the house--ploop, ploop. And of course since chickens are flock animals, you will not have just one, but at least TWO chickens pooping around the house--ugh! Calling that "not ideal" is a bit of an understatement.
Are you thinking of house-training your inside chicken? Well, we've heard of people who have done that. But don't plan on it--really. You need extraordinary skill, and all the time in the world. It's not like house training a dog. Or maybe it could be, sorta, IF you're picturing training the most stubborn dog you can imagine, one that poops five or more times a day, one that will always have a few accidents, one that can fly and perch on the top of your head or computer or kitchen counter... and if you're picturing training at least two of them. And housetraining them won't solve the issue of providing them with good foraging opportunities that will satisfy their natural instincts.
Occasionally we hear from people who want to keep an indoor pet chicken in a large cage, thinking that if birds like parrots are kept that way, then why not chickens?
Well, here's why not: Parrots, of course, don't lay 300 eggs a year as chickens do. Chickens literally need sunlight for their health. Sunlight will help your hens produce eggs; they need the light to help them metabolize calcium for shells, and day length stimulates them to lay. Chickens also love to sunbathe; they will lay outside on one side and stretch out a wing to absorb all the warmth and sunlight they can. And changing light triggers molting in the fall as the days grow shorter. If your chicken is kept inside without changing day-lengths, their annual molting cycle can be seriously thrown off. Plus, while chickens do fly for short distances, they are chiefly ground-dwelling birds. They don't spend their days flitting from branch to branch in tree-tops; they want to be on the ground foraging for food. They will not want to be sitting on a perch in a cage all day. So, if you keep your chickens in a wire-floored cage, it can even cause problems with their feet. The wire doesn't allow their nails to wear naturally. On the other hand, if the floor of the cage has bedding (like you would have in an outside coop/run set-up), instinct drives them to scratch through it, which will fling it (along with their droppings) all over your floor anyway. Finally, chickens produce far more waste (poop) than parrots or other indoor "caged birds" do, since chickens must eat so much for their bodies to produce the number of eggs they do. Keeping a chicken is just not like keeping a parrot at all!
So the bottom line is that although it is not completely impossible to keep indoor pet chickens, they have many requirements that make it difficult and time-consuming to do in a way that gives them a good quality of life, and allows you to keep your home sanitary and clean for your family.