see Columbus on a map
 Layman's version:
You can only keep chickens if you have a lot of 2 acres or more. If you have a lot that big, you can keep up to 32 chickens there.
 The Urban Chicken ordinance on the books:
Link to municipal code online
Sec. 5-42. Keeping of fowl.
(a) When permitted. The keeping of fowl shall be allowed as an accessory use on any lot two acres or more in size. The keeping of such domestic fowl shall be in accordance with the following:
(1) The number of domestic fowl kept on a given lot shall not exceed the ratio of one bird unit per one acre, with a bird unit identified as follows:
32 chickens equals one bird unit.
16 ducks equals one bird unit.
8 turkeys equals one bird unit.
8 geese equals one bird unit.
(2) When determining the number of domestic fowl permitted, only fowl six weeks or older in age shall be counted.
(b) Compliance with zoning ordinance. The keeping of racing, homing or exhibition (fancy) pigeons shall be allowed as an accessory use of a residential lot only in accordance with the "minimum requirements" set forth in the zoning ordinance and the distance from adjacent dwelling requirement established by paragraph (c)(3) of section 5-42.
(c) Location of accessory structures. All accessory structures associated with the keeping or housing of animals shall be located in accordance with the provisions stated as follows:
(1) Barns or other structures used in connection with agriculture, to include structures for the keeping, confining or sheltering of any poultry as defined in subsection (a)(1) above, shall be located no closer than 100 feet to any lot line. In no instance shall such structures be used for retail sales, except as permitted under the business license section of this Code.
(2) Barns or other structures used for the confining or sheltering of domestic fowl not in connection with agriculture shall be no closer than 50 feet to any lot line.
(3) Cages, lofts, pens and other structures which are used for the keeping of homing, racing or exhibition (fancy) pigeons shall be located no closer than 150 feet from the nearest part of a house occupied by a person other than the keeper of the birds.
(d) Fowl commonly excepted. Subject to the provisions of paragraph (f) of this section, exotic chickens, ducks and geese six weeks old, birds such as canaries, parakeets, doves, and parrots or other exotic birds normally kept as pets or primarily for hobby purposes shall not be subject to the remaining provisions of this section.
(e) Businesses excluded. Retail stores properly licensed under other provisions of this Code which maintain exotic chickens, ducks and geese six weeks of age, canaries, parakeets, doves, parrots, and other exotic birds for the purpose of retail sales from inventory, and other properly licensed poultry related industries other than retail sales to pet owners shall not be subject to the provisions of this section, except for paragraph (f).
(f) Noise and odors. Notwithstanding any of the provisions contained herein, at no time shall an owner of domestic fowl place a structure or keep domestic fowl in any fashion which would cause emission of noise or odor detrimental to other property or individuals residing thereon in the area. Further, it shall be unlawful to allow domestic fowl or other exotic fowl or birds to run on public property or private property other than the property of its owner.
(g) Notice of violation. Any owner of birds or fowl in Columbus, or any owner of property used for the keeping of birds or fowl in the city, shall be notified in writing of any violation of this section by the department of public services or the health department, and shall be given 30 days to correct stated violation. If after 30 days from the date of the notice, the owner of the birds or fowl or the property owner or occupant of the premises where the birds or fowl reside fails to comply with the provisions of this section, a citation to appear in the recorder's court may be issued to such person.
(Ord. No. 85-118, § 1, 10-15-85)