Cityegger,
I can sympathize. I kept chickens and geese as a child, and even got permission from my university to bring my beloved pair of bantams and their coop with me (it was a state u with an agricultural college, and a barn behind my dormitory!). When I later had to live in a small apartment for nearly 10 years, where no pets except fish and small animals (hamsters, budgies, etc.) were allowed, I almost went crazy. When I bought my house, my choice was based on having woods in back, and a small barn.
My advice, if you must have chickens, is to get a pair of bantam pullets. Breeds such as Old English Game Bantams (OEGB), Seramas, Belgian D'Anvers, and several others are about the size of a pigeon.
Buy the biggest rabbit hutch you can get into your apartment, one that has a shelter box in it and a metal tray to catch droppings below. Get a parrot perch that you can position in the hutch, since chickens need to roost. Line the bottom of the hutch with heavy paper and use shavings. Get a toddler's playpen with mesh sides, and put shavings in that, and a cat litterbox with play sand (you can buy it at Home Depot and Lowe's -- fine texture sand) for dust baths. Throw treats in and let them enjoy the space during the day. You can put it near a sunny window if you have one, so they can sunbathe.
You'll need a good vacuum cleaner and Dustbuster to keep the area tidy, but so what?
My 2 pennies' worth!