Personally, I would not. It would be unhealthy for your family, and also unhealthy for the chicken.
For you:
1. Chickens shed an incredible amount of dander. This is a very fine silty dust that is also very oily in nature. It covers ALL surfaces, including vertical ones. Highly allergenic as well as a cleaning nightmare.
2. Chickens are noisy. A hen/pullet in midst of egg song rivals any roo in voice volume. And her egg song will last longer than any roo crow.
3. Chickens are messy. Their very nature says they are designed to want to dig, need to dig, want and need to peck at everything in their environment.
4. Chickens need to perch. And she will, where ever she wants to. Even if she is wearing a diaper, she will fly around, and land on what ever she chooses to. Can break a lot of stuff.
5. Chickens poop. A lot. While regular poop is not THAT smelly, a cecal poop is smelly to the ultimate degree. It's the texture of greasy chocolate pudding. Even if she wears a diaper, those cecal poops will stink up your house A LOT. If she does wear a diaper, the poo in the diaper will mess up her feathers a LOT, and you will have to wash her a LOT. Not healthy for her skin or her feathers.
For her:
1. chickens are flock animals. They were created and need to be part of a flock to meet their social needs.
2. chickens are farm animals. While they do funtion well in a back yard flock, they have the same basics that they would have while living on a farm.
3. Chickens need to be able to dust bathe. It's necessary for their skin and feather health, as well as keeping them clear of mites/lice.
4. Chickens need to dig in the dirt, chase and bugs, eat greens. They eat soil, grit, and plenty of other things that you might consider to be quite disgusting and that would not be found in your house.
5. Lack of sunlight. Not healthy for her skin or feathers. Need vit D which is manufactured by sunlight to be able to process calcium. Without it, her egg shells will be weak, may also play a role in egg binding and other reproductive issues. chickens live by day night cycles. Do you want to get up at 4:30 AM when she does? She will begin calling then! If you treat her like a pet bird

utting her to bed at your convenience, that will mess with her pituitary, possibly sending her into random molting cycles, as well as messing with her laying cycles.
6. If you do not provide the necessities for her to act like a chicken ALL THE TIME, she is likely to develop some very psychotic behaviors which may include: chronic feather picking. Stressed birds often pull their own feathers and self mutilate themselves. Very loud calling... all the time: trying to call her non existent flock mates.
If you intend to keep a chicken, I suggest that you provide a coop and run in your yard that is at least 4 s.f. in coop, and 10 s.f. in yard per bird, and that you have at least 2 birds.