I'm sorry you're in this situation, but I agree with the other posters that i this case, "rules are rules." You'd have been in a better position if you had sought to get the rules changed to allow a small number of birds before you got them.
HOA rules are rarely like municipal ordinances. Municipal ordinances can become out-dated, community opinions change, and things like keeping chickens in your backyard, which was out of favor for quite some time, come back into favor.
People who buy in HOA neighborhoods *want* rules to limit what their neighbors do. HOAs are generally less flexible than your average town council, and more political. There's an entire community near us that requires a permit and inspection by an HOA compliance inspector before you can paint anything on the exterior of your house, get new shingles on your roof, or put in a flower bed that isn't in the back yard. The HOA fees are exhorbitant, and the HOA agreement and rules are about 400 pages. We'd considered buying a rental property there a while back, and decided there was no way we would deal with that level of bovine fertilizer.
I rented in an HOA community once, that was bad enough. We were straight out of college at the time, and had a bit of fun with finding crazy things we *could* do just to annoy our neighbor ... like getting 20 pink lawn flamingos ... and having several big hairy dudes hang out in lounge chairs in the front yard drinking beer when the neighbor had an open house whiile his house was for sale ... because we were sure he'd stolen the lawn flamingos. If I were you, I'd plan on moving.
Good luck, but odds are, you're going to need to find a home for your chickens before you can get the rules changed. Got anyone who can give them a temporary home, so that you can go in "birdless" and try to get the rules ammended? Got any friends amongst your neighbors who have lived in the neighborhood a long time, and would be willing to side with you?