Well, it's not a good idea, but you can, according to the New York Daily News. They've got a story about Robert McMinn and Jules Corkery, who are raising three hens in their one bedroom in Queens.
The Serama hens, a small domesticated breed that typically weighs about a pound, nest in a converted ferret cage in the living room, McMinn said.
They have the run of the apartment — except for the bedroom — and lay about two eggs each a week. They also have a litter box of sand so they can give themselves cleansing dust baths.
But "they poop everywhere," said McMinn, who uses the droppings to fertilize the soil in nearby community gardens.
The two give talks about urban chicken-raising at their local library, and McMinn also hosts a radio program called the Bucky Buckaw Backyard Chicken Broadcast. But they're quick to make it clear that they don't recommend raising the birds indoors. Chickens need to give themselves dust baths. They need to eat bugs. And, again, they need to poop everywhere all the time. All these things are less messy outside.
It can be a tall order to find a New York apartment with yard access, though, so if you absolutely must share studio space with your chickens, it's essential to give them sand to bathe in, take them outside regularly, get them adequate sunlight and room to exercise, and maybe look into bird diapers.