Using an ab initio total energy approach, we study the stability of free and Ag(111)-supported MgO(111) ultrathin films. We unravel a novel microscopic mechanism of stabilization of polar oxide orientations, based on a strong modification of the MgO structural phase diagram with respect to the bulk material. We predict that, at low thickness, films which are either unsupported or deposited on Ag(111) display a graphitelike Bk structure rather than the expected rocksalt one. Our results provide a consistent interpretation of recent experimental findings, exemplify the efficiency of this novel stabilization mechanism, and suggest new methods to engineer oxide nanostructures.