Chickens in Chicago

I learned last night while surfing around that you can keep laying hens in Chicago! I'm amazed there isn't some crazy law here prohibiting it. I found a blog by someone who keeps a few chickens in her backyard. I'm totally curious. It would be great to have fresh eggs. Could we keep chickens on the balcony? Our new place actually has poultry potential thanks to a large balcony. Hmm... Some research is in order.