The observation of superconductivity in doped C60 has attracted much attention, as these materials represent an entirely new class of superconductors. A maximum transition temperature (Tc) of 40 K has been reported for electron-doped C60 crystals, while a Tc of 52 K has been seen in hole-doped crystals; only the copper oxide superconductors have higher transition temperatures. The results for C60 raise the intriguing questions of whether conventional electron-phonon coupling alone can produce such high transition temperatures, and whether even higher transition temperatures might be observed in other fullerenes. There have, however, been no confirmed reports of superconductivity in other fullerenes, though it has recently been observed in carbon nanotubes. Here we report the observation of superconductivity in single crystals of electric-field-doped C70. The maximum transition temperature of about 7 K is achieved when the sample is doped to approximately four electrons per C70 molecule, which corresponds to a half-filled conduction band. We anticipate superconductivity in smaller fullerenes at temperatures even higher than in C60 if the right charge density can be induced.