We report that the chalcohalide compound Tl6SeI4 is a promising material for efficient X-ray and gamma-ray detection. This material has a higher figure of merit than the current state-of-the-art material for room-temperature operation, Cd0.9Zn0.1Te (CZT). We have synthesized high-quality single-crystalline wafers of Tl6SeI4 with detector-grade resistivities and good carrier transport of both electrons and holes. We demonstrate that pulse height spectra recorded using Co-57 radiation show an energy resolution matching that of a commercial CZT detector material.