Legal Question in Real Estate Law in California

Usually, no. A contract requires: offer, acceptance and consideration. While it sounds as though you, without going into greater detail, may have an offer and acceptance, there is no consideration changing hands, and therefore, you have no contract.

Mr. Truitt is correct that technically there must be consideration, even though it can be something very small and worth next to nothing [classical English law allowed it to be a pepper corn because most people could not read but could observe the transfer of a physical object--a pepper corn is the little nut like seed/nut that is crushed to make the spice pepper from]. In your case, the HOA has a rule that unit modifications can not be made without the approval of the HOA ruling Board; having received their approval, you now have the right to d what they agreed to let you do. Whether this is a contract or that you can argue they are estopped from arguing that you can not make the change is largely irrelevant. There is an agreement on their part as to what they actually agreed to and they can not go back on it.