The motion of electrons through quantum dots is strongly modified by single-electron charging and the quantization of energy levels. Much effort has been directed towards extending studies of electron transport to chemical nanostructures, including molecules, nanocrystals and nanotubes. Here we report the fabrication of single-molecule transistors based on individual C60 molecules connected to gold electrodes. We perform transport measurements that provide evidence for a coupling between the centre-of-mass motion of the C60 molecules and single-electron hopping--a conduction mechanism that has not been observed previously in quantum dot studies. The coupling is manifest as quantized nano-mechanical oscillations of the C60 molecule against the gold surface, with a frequency of about 1.2 THz. This value is in good agreement with a simple theoretical estimate based on van der Waals and electrostatic interactions between C60 molecules and gold electrodes.