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Up to 10 chickens if your lot is at least one-half of an acre. Less than half an acre and no chickens would be allowed.
The Urban Chicken ordinance on the books:
Link to municipal code online: Redmond Municipal Code, Chapter 7.04.156
Text of municipal code
7.04.156 Small domestic animals.
(a) Types. Small domestic animals (mammals and fowl) include rabbits, ducks, geese, swans, chickens and other similar animals. Mink, hogs, large domestic animals and household pets are excluded.
(b) Limitations. In residential districts, no more than ten small domestic animals may be kept on a minimum lot size of one-half acre. In A and G districts, there shall be no limit on the number of small domestic animals kept.
(c) Shelter. Small domestic animals shall be sheltered in a suitable, clean structure which shall be located at least thirty feet away from any property line.
(d) Confinement. Adequate measures shall be taken to prevent animals from straying onto adjacent property. (Ord. 1442 § 5, 1988).