First, read your CC&R's. If they disallow poultry or fowl or chickens, you're stuck, regardless of the ordinances. In Arizona "livestock" does not include non-mammals. However, if they disallow livestock, you may have to fight to prove that chickens are not livestock. And if there is a definitions section that includes them as livestock, then they are as far as the CC&Rs are concerned. Drive through your neighborhood. Do other people keep chickens or goats or sheep or horses or cattle or turkeys or geese? Cannot legally enforce against one person when it has not been enforced against others.
Is San Tan Valley incorporated? If so, check their zoning ordinances and city code. If not, check your county zoning and ordinances. Chances are pretty high that the county will allow, but you need to verify it yourself.