The observation of superconductivity in the layered transition metal oxide NaxCoO2 y H2O (K. Takada et al., Nature 422, 53 (2003)) has caused a tremendous upsurge of scientific interest due to its similarities and its differences to the copper based high-temperature superconductors. Two years after the discovery, we report the fabrication of single-phase superconducting epitaxial thin films of Na0.3CoO2 x 1.3 D2O grown by pulsed laser deposition technique. This opens additional roads for experimental research exploring the superconducting state and the phase diagram of this unconventional material.