Layman's version:
A total of not more than six hens (in combination with other animals) in a sanitary pen no less than 40 feet from neighboring residences.
 The Urban Chicken ordinance on the books:
Link to municipal code online: Chapter 5 Animals and Fowl
Chapter 5 ANIMALS AND FOWL*
5.01.020 Keeping of chickens, pigeons or rabbits.
It is unlawful for any person to keep or maintain within the city, or permit to be kept or maintained upon land belonging to such person, any chickens, pigeons or rabbits except as follows:
A total of not more than six chicken hens or six pigeons or a combination of chicken hens and pigeons not to exceed the number of six, or a total of not more than six rabbits may be kept and maintained in a clean and sanitary pen or structure, no part of which shall be located less than forty feet from any residence, other than a residence owned and occupied by the person owning or in possession of such animals; and, provided further, that the keeping of such animals shall not create a health or nuisance problem. (Code § 8-2.102.)