THE presence of apical oxygens (above or below the CuO2 planes) has been regarded as indispensable for the occurrence of hole-doped superconductivity in the high-transition-temperature (high-T-c) copper oxide superconductors(1,2). We have opposed this view(3,4), on the basis of studies in compounds such as (Ca, Sr)(1)-xCuO2-(y) and Srn+1CunO2n+1+1+delta; however, our conclusions have been questioned in subsequent Work(5,6). Here we provide strong evidence for hole-doped superconductivity in the absence of apical oxygens, by showing that Ca2CuO2Cl2 can be rendered superconducting by doping with sodium. The compound contains CuO2 planes as in La2CuO4, but all of the oxygen atoms at the apices of tbe CuO6 octahedra found in La2CuO4 are replaced by chlorine, and the lanthanum atoms by calcium(7). The apparent difference in mass and electronic character between chlorine and oxygen might strongly affect the electronic structure of the CuO2 planes if the contributions of the apical atoms were significant. But we find hole-doped superconductivity in (Ca, Na)(2)CuO2Cl2 at rather high transition temperatures (26K at maximum), which are only slightly less than those of doped La2CuO4 (ref. 8). This implies that the apical atoms do not play a significant role in the electron pairing mechanism leading to high-T-c superconductivity.