Communication: The growth mode and structure of superconducting films of Hg-1223 (HgBa2Ca2Cu3O8+delta) are described. The results from atomic force microscopy and X-ray studies are presented and the implications for the unit cell discussed. The positions of the atoms relative to the substrate Y0.10Zr0.85O1.93 are calculated by computer simulation-showing that the growth is epitaxial. Hg-1223 is a member of the family of superconducting cuprates HgBa2Can-1CunO2n+2+delta, which are important for both science and technology.