Layman's version:
25 chickens allowed if they are kept 15 ft. from neighboring dwellings. Roosters are allowed but subject to noise nuisance violations.
 The Urban Chicken ordinance on the books:
Link to municipal code online: Title 7: Public Safety, Health and Welfare
Text of municipal code:
7.32.060 Cleanliness of premises where animals are kept.
Every person owning or occupying premises where any animal, fowl, or bird is kept shall keep the stable, barn, stall, pen, coop, building or place in which the animal is kept in a clean and sanitary condition. (Ord. 161 N.C. (2d) § 33 (part), 1973.)
7.84.020 Specific prohibitions.
In addition to and separate from the prohibition set forth in Section 7.84.010 above, the following acts, and the causing or permitting thereof, are hereby declared to be in violation of this ordinance. As used in this section, the term “noise disturbance” means any sound which (1) endangers or injures the safety or health of humans or animals; (2) annoys or disturbs a reasonable person of normal sensitiveness; or (3) endangers or injures personal or real property. The listing of specific prohibited activities in this section is not intended to limit the city’s authority to regulate any and all loud, unnecessary and unusual noise pursuant to Section 7.84.010. Any noise not falling within the specific prohibitions set forth in this section is subject to regulation under the provisions of Section 7.84.010 above....
C. Animals and Birds. It shall be unlawful for any person owning, possessing, or harboring any animal or bird to allow said animal or bird to howl, bark, meow, squawk, or make other annoying noises continuously and/or incessantly for an unreasonable period of time so as to create a noise disturbance across a residential real property line. For purposes of this subsection, the animal or bird noise shall not be deemed a noise disturbance if a person is trespassing or threatening to trespass upon private property in or upon which the animal or bird is situated, or is using any other means to tease or provoke the animal or bird. This provision shall not apply to a zoo or animal theme park.
<NOTE: as of 10/13/09, cannot find exact text allowing up to 25 chickens>