Does the C.A. have poultry-keeping rules that are different from the County's? If not, your biggest problem will be distance from other houses.
We live in Ellicott City and we're zoned "R-20" according to the Howard County "My Neighborhood" map. In that zone, "farming" is permitted, provided that on a lot of less than 40,000 square feet, no fowl other than for the normal use of the family residing on the lot and no livestock. You can find the map here: http://gis.howardcountymd.gov/PublicGISOnline/MyNeighbor.aspx
Unfortunately, Sect. 128-A(4) says that in all districts where farming is permitted, the following shall not be allowed within 200 feet of an existing dwelling on a lot:
a. An animal shelter including a building, shed, roofed structure or moveable shelter that houses or provides protection for animals other than household pets; ...
So you can only have a coop if there are no dwellings within 200' of the coop's location. I'm pretty sure that includes your own home. And I believe the number of chickens is limited to 8, but that should be plenty for personal use.
(Big thanks to my sister who is a planner for another county and did the research for me!)