As long as your city zoning laws allow chickens, you should be good to go. You should no more be required to talk to the neighbors to get their approval for getting chickens than you should be required to talk to the neighbors for their approval before you get a dog. Obey the letter of the law regarding numbers, and distance from neighbor's property. Don't get a rooster. Build your coop and run to keep them secure (do some thread searches regarding predator proofing).
Human nature being what it is, you might want to be sure that your run is not directly accessible from the street or sidewalk. Some humans have a cruel or stupid streak, and will harass animals simply b/c they can get away with it. An other poster had chickens at a school, and had issues with the kids tossing dangerous objects into the chicken run, and harassing them. I would build a completely enclosed run out of 1/2" hardware cloth. Be sure you follow the recommended coop run space of 4 s.f. in coop and 10 s.f. in run minimum per bird.