We discovered superconductivity at 4.8 K in the hexagonal layered compound La2IRu2 comprising a triangular lattice of the La and a honeycomb lattice of the Ru atoms. First-principles calculations reveal a two-dimensional band structure made up of La 5d and Ru 4d electrons and formal oxidation states +1.5 for the La and the uncommon oxidation state -1 for the Ru atoms. The temperature dependence of the specific heat indicates fully gapped superconductivity. Nevertheless, the upper critical field of this compound violates the Pauli limit. We argue that the high upper critical field is ascribed to an antisymmetric spin-orbit coupling in the unique multilayer structure.