Mg10Ir19B16, a previously unreported compound in the Mg-Ir-B chemical system, is found to be superconducting at temperatures near 5 K. The fact that the compound exhibits a range of superconducting temperatures between 4 and 5 K suggests that a range of stoichiometries is allowed, though no structural evidence for this is observed. The compound has a large, noncentrosymmetric, body centered cubic unit cell with a = 10.568 Angstrom, displaying a structure type for which no previous superconductors have been reported.