The theory of hole superconductivity explains high temperature superconductivity in cuprates as driven by pairing of hole carriers in oxygen pπ orbitals in the highly negatively charged Cu − O planes. The pairing mechanism is hole undressing and is Coulomb-interaction driven. We propose that the planes of B atoms in M gB2 are akin to the Cu − O planes without Cu, and that the recently observed high temperature superconductivity in M gB2 arises similarly from undressing of hole carriers in the planar boron px,y orbitals in the negatively charged B − planes. Doping M gB2 with electrons and with holes should mirror the behavior of underdoped and overdoped high Tc cuprates respectively. We discuss possible ways to achieve higher transition temperatures in boron compounds based on this theory.