Despite the remarkable rise in efficiencies of solar cells containing the lead-halide perovskite absorbers RPbX3 (R = organic cation; X = Br(-) or I(-)), the toxicity of lead remains a concern for the large-scale implementation of this technology. This has spurred the search for lead-free materials with similar optoelectronic properties. Here, we use the double-perovskite structure to incorporate nontoxic Bi(3+) into the perovskite lattice in Cs2AgBiBr6 (1). The solid shows a long room-temperature fundamental photoluminescence (PL) lifetime of ca. 660 ns, which is very encouraging for photovoltaic applications. Comparison between single-crystal and powder PL decay curves of 1 suggests inherently high defect tolerance. The material has an indirect bandgap of 1.95 eV, suited for a tandem solar cell. Furthermore, 1 is significantly more heat and moisture stable compared to (MA)PbI3. The extremely promising optical and physical properties of 1 shown here motivate further exploration of both inorganic and hybrid halide double perovskites for photovoltaics and other optoelectronics.