Epitaxial MgO thin films were grown on Si(001) by pulsed laser deposition. In spite of a large (-22.5%) lattice mismatch, epitaxy occurs with alignment of all crystallographic axes. Epitaxial quality and deposition rate are both sensitive to temperature and oxygen pressure. We believe this is the first demonstration of epitaxial MgO on Si. We employ MgO intermediate layers for superconducting epitaxial YBa2Cu3O7-δ/ BaTiO3 thin films on Si with a critical current density of 6.7×105 A/cm2 at 77 K.