RECENT work(1,2) has shown that superconducting copper oxyhalides can be synthesized, with the La2CuO4 structure but with no oxygen in the ’apical’ positions outside the CuO2 planes. For these materials to be rendered superconducting, charge carriers must be introduced into the CuO2 planes; in previous work, positive carriers (holes) have been introduced by the incorporation of interstitial fluorine in Sr2CuO2F2+delta (transition temperature T-c = 46 K)(1), or by the substitution of sodium for calcium in (Ca,Na)(2)CuO2Cl2 (T-c = 26 K)(2). Here we present an alternative doping approach for this copper oxyhalide family : holes are introduced by partially replacing the (monovalent) halogen that occupies the apical sites with (divalent) oxygen. We have obtained bulk superconductivity with T-c above 77 K in a new double-layer compound (Sr,Ca)(3)Cu2O4+deltaCl2-y, which is isostructural with (La,Sr)(2)CaCu2O6 (ref. 3), with (Sr,Ca) at the (La,Sr) or Ca sites, and Cl at the apical sites outside the CuO2 planes.