I have 5 acres, but only 1 acre is open. I have 6 chickens. I think it's recommended that they each have a minimum of 10 square-feet in the run, so if you've got more than that, you're fine.
Yes, definitely check your zoning ordinances! Neighbors are always nice in the beginning, but there are countless stories here on BYC where something upsets them and they decide to file a complaint. Protect yourself and your flock by knowing the laws in your town.