Single-molecule transistors are currently attracting enormous attention as possible quantum information processing devices(1-5). An intrinsic limitation to their prospects, however, is associated with the presence of a small number of quantized conductance channels, each channel with a high access resistance of at best R-K/2 = h/2e(2) = 12.9 k Omega. However, when the contacting leads become superconducting, long-range correlations can extend throughout the whole system by means of the proximity effect. This not only lifts the resistive limitation of normal-state contacts, but further paves the way to probe electron transport through a single molecule. Here we demonstrate the realization of superconducting single-molecule transistors involving a single C-60 fullerene molecule. In the past few years, we have seen gate-controlled Josephson supercurrents induced in the family of low-dimensional carbon structures such as flakes of two-dimensional graphene(6) and portions of one-dimensional carbon nanotubes(7). The present study, involving a full zero-dimensional fullerene, completes the picture.