Photo by Lost Albatross

Bottom line:
You may keep chickens, and all kinds of other animals it turns out, as long as they are kept in enclosures at least twenty-five feet from neighboring homes. They don't have to be twenty-five feet from your home -- just your neighbor's home. And the enclosures must be cleaned regularly. No mention of a limit on the number of chickens allowed.

For more details or with specific questions, contact:
(or see the fine print below)
Berkeley Animal Care Services
2013 Second St.
(510) 981-6600

Fine print: (see Berkeley's Municipal Code and Zoning Ordinance City of Berkeley Title 10 )

10.12.040 Rabbits, domestic fowl, etc.--Enclosure requirements.
It is unlawful for any person to keep on any premises owned, occupied or controlled by him in the City any rabbits, guinea pigs, or any chickens, ducks, pigeons, geese, turkeys or other domestic fowl, unless such fowls or animals are kept in an enclosure, no part of which is within twenty-five feet of any dwelling house occupied by human beings; provided, however, that the dwelling house referred to above does not mean the house in which the person resides who keeps the fowls or animals; provided that any of said fowls or animals may be kept temporarily for purpose of sale at any shop or place of business where the same are bought, sold or dealt in. (Ord. 2533-NS (part), 1942: Ord. 557-NS § 7, 1918)

10.12.060 Rabbits, domestic fowl, etc.--Sanitary maintenance of coops or enclosures required.
All coops and enclosures in which any fowls or animals referred to in Section 10.12.040 are kept, must be maintained in a sanitary manner, and be regularly cleaned, in order to prevent any accumulation of manure or offal. (Ord. 2533-NS (part), 1961: Ord. 557-NS § 8, 1918)