The observation of superconductivity in the layered transition metal oxide NaxCoO2∙yH2O [K. Takada et al., Nature (London) 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∙1.3D2O 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.