Graphene can be grown directly on MgO(111) by industrially practical and scalable methods: free radical-assisted chemical vapor deposition (CVD), and physical vapor deposition (PVD). Single layer and double layer films can be produced by PVD, with a ~ 2 monolayer (ML) thick film as the apparent limiting thickness. C(1s) x-ray photoemission spectra (XPS) indicate that in both layers, carbon atoms are in two different oxidation states. Low energy electron diffraction (LEED) data are consistent with this, showing unequal graphene A site/B site intensities for both single and double layer graphene, yielding C3V symmetry. This lifts the A site/B site chemical equivalence in the graphene lattice, and therefore also the HOMO/LUMO degeneracy at the Dirac point. Consistent with this, a band gap of ~ 0.5 -1 eV has been observed for the two layer film. The XPS, LEED and band gap findings indicate that the graphene/MgO interface is commensurate, and that the MgO surface layer is reconstructed, resulting in carbon→MgO charge transfer. In addition, graphene growth by PVD is self-limiting at 2 monolayers thickness. These findings have implications for graphene growth on other (111) oxide surfaces. The ability to grow MgO(111) films on Si(100)-reported in the literature- points to a direct path to the development of graphene-based field effect transistors (FETs) and spin-FETs on MgO(111)/Si(100).