STARTING with the pioneering work of Bednorz and Müller1, many copper-oxide-based superconductors with high transition temperatures (T c) have been discovered. All contain layers of copper-oxygen squares, pyramids or octahedra as their electronically active structural components2,3. One structure type, first reported for La2SrCu2O6 and La2CaCu2O6 (ref. 4), has stood as an enigma since the beginning of high-T c research. This crystal structure4-7 (Fig. 1) is the least complex of all the structures with the double layers of copper oxide pyramids common to the compounds with highest T c, yet despite considerable effort, both published8,9 and unpublished, it has not until now been made superconducting. Here we report the successful synthesis and preliminary physical characterization of superconducting (La, Sr)2CaCu2O6. The highest transition temperature observed is 60 K at the composition La1.6Sr0.4CaCu2O6. This is a uniquely simple double-layer superconductor, which, like its single-layer analogue (La, Sr)2CuO4, becomes superconducting through the introduction of carriers in an unambiguous manner-by straightforward atomic substitution without the intervention of charge reservoir layers with flexible valence states.