I live in the center of Omaha, literally two blocks from Dodge street. Chickens are allowed within city limits, if certain requirements are met. It's all spelled out in the City's Municiple Codes. Just Google "city of omaha municiple codes" and look under pets or livestock. I pasted a few of the specifics below.
Basically if you want to keeps chickens, call the Douglas county health department and request an application to keep poultry on your property. They'll mail it within a week or so. Fill it out, send it in, and someone will call you to say that they are coming to your home to "inspect the place where you plan to keep your poultry". I just built a 4x6ft coop with a 6x8ft run attached. It is fully enclosed, even with chicken wire on top of the run. The health department wants to know how many you plan to keep, where you'll keep them, etc. Three of the four sides of my property are fenced, but they required that I fence the fourth side (I just used a metal wire fencing, slightly stiffer than chicken wire). It was good enough for them. The permit is good for one calendar year beginning January 1. Oh, and if you live in a neighborhood with covenants that prohibit poultry, then you're out of luck. And lastly, no roosters allowed. That's about it. Easy as pie. I just got my first 3 hens about a week ago.
Good luck!
Sec. 6-263. Poultry to be enclosed.
It shall be unlawful for any person to allow poultry, chickens, hens, turkeys, ducks, geese, or other like fowl to be at large within the city, except in enclosed places on private property.
Sec. 6-267. Application.
Any person desiring to obtain a permit required by the provisions of this division shall make application therefor in writing on a form furnished by the health department stating:
(a) The name and location of the applicant.
(b) The kind and number of animals or fowl to be kept.
(c) The name of the person in charge of the animals or fowl, if different from the name and location of the applicant.
(d) Such other information as the department may require.
Sec. 6-271. Duration.
All permits issued under the provisions of this division shall be valid for a period of one year, running from January 1 to December 31.
