First, you need to thoroughly read and understand your documents: CC&Rs, Bylaws, Articles of Incorporation, Rules and any others that may exist. You need to know who has the power to change the provisions in whatever document or documents disallow chickens. You need to look at the specific language used, and you need to review any provisions relating to any and all other animals.
If (as would be common) the CC&Rs disallow chickens, chances are that the board does NOT have the power to override those provisions or alter the document to llow them. Generally ONLY the membership can alter the CC&Rs, and it usually requires a huge percentage of approving votes--think of it as being similar to amending the constitution. What the board CAN do is recommend a change, and schedule an election for the members to vote on the issue. Even if htey say "no," chances are pretty good that either your documents or your state law details a process where you can force an issue to a membership vote. This would usually involve a perentage (in Arizna it is 20%) of the membership requesting via petition a vote.
However, there are SOME CC&Rs that have no built-in provision for change/amendmemnt, meaning that only is 100% of the membership votes to approve a change can it be incorporated. Documents written without provisions for change usually either expire after 20 or so years, or self-renew every twenty or so years, with a provision that the year they are due to expire or renew, changes can be incorporated by a majority (or other stated approval percentage) of the members.
So, back to my first sentence--first you neeed to find out what you are up against. Then we can give you some ideas. The best presentation in the world will not help if it is not in the power of the board to make your recommended change.
