Superconductivity was first observed more than a century ago, but the search for new superconducting materials remains a challenge. The Cooper pairs in superconductors are ideal embodiments of quantum entanglement. Thus, novel superconductors can be critical for both learning about electronic systems in condensed matter and for possible application in future quantum technologies. Here two previously unreported materials, NbIr 2 B 2 and TaIr 2 B 2 , are presented with superconducting transitions at 7.2 and 5.2 K, respectively. They display a unique noncentrosymmetric crystal structure, and for both compounds the magnetic field that destroys the superconductivity at 0 K exceeds one of the fundamental characteristics of conventional superconductors (the "Pauli limit"), suggesting that the superconductivity may be unconventional. Supporting this experimentally based deduction, first-principle calculations show a spinsplit Fermi surface due to the presence of strong spin-orbit coupling. These materials may thus provide an excellent platform for the study of unconventional superconductivity in intermetallic compounds.