Hi! I'm new to this site so feeling my way through. I don't have any personal experience with chickens as of yet. I do have a lot of experience with home owner associations and CC&R's. This is from where my message originates.
In my HOA we have had neighbors with chickens and roosters so the subject has been discussed. Roosters had to go, no further discussion. Our city ordinances permit back yard chickens so our HOA board of directors decided that if a homeowner requested permission to have the chickens it would be okay as long as they followed the city ordinance.
You might familiarize yourself with your HOA governing docs so you have a thorough understanding of them and can easily paraphrase what they say. You will be the informed homeowner. Also do that with the city / county ordinance specific to backyard chickens. There are a lot of board of directors who haven't a clue but rather have an agenda as to how they want their HOA governed. If your HOA references city and county ordinance for specific types of permits, i.e. fences, roofs, encroachment to sidewalks, etc. use that as an example to your benefit. If they balk push the point diplomatically (of course) why they would adopt some city / county ordinance but reject others. Canvas your neighbors, write up a simple petition for the backyard chickens, get signatures. Again, read your governing docs cause homeowners have rights, you just have to know how to do it legally within your HOA.
Hope this helps!