Hated having chicks in the house. 4 hens in a basement will be a proper cleaning commitment. I suppose you have to consider if it’s really fair on the hens too.
I’d be worried about ventilation. Chickens indoors are going to produce a lot of dust and dander. If you keep on top of cleaning out, you may keep ammonia down. There’s also the noise. Are you allowed to keep chickens inside? Or do outdoor laws not apply inside?