It all depends on how large the house is and how many Greeks it is going to accomodate as to how much it costs to build. Yes, you definitely have to have permission to start building one. I know that DZ has to get approval from Headquarters before building. My brother is a member of KA and they are in the process of building a new house right now. They had to get city permits, school approval, etc. A lot of red tape to go through before building occurs!