Superconductivity in the extreme two-dimensional limit is studied on ultrathin lead films down to two atomic layers, where only a single channel of quantum well states exists. Scanning tunneling spectroscopy reveals that local superconducting order remains robust until two atomic layers, where the transition temperature abruptly plunges to a lower value, depending sensitively on the exact atomic structure of the film. Our result shows that Cooper pairs can still form in the last two-dimensional channel of electron states, although their binding is strongly affected by the substrate.