The development of manipulation tools that are not too 'fat' or too 'sticky' for atomic scale assembly is an important challenge facing nanotechnology. Impressive nanofabrication capabilities have been demonstrated with scanning probe manipulation of atoms and molecules on clean surfaces. However, as fabrication tools, both scanning tunnelling and atomic force microscopes suffer from a loading deficiency: although they can manipulate atoms already present, they cannot efficiently deliver atoms to the work area. Carbon nanotubes, with their hollow cores and large aspect ratios, have been suggested as possible conduits for nanoscale amounts of material. Already much effort has been devoted to the filling of nanotubes and the application of such techniques. Furthermore, carbon nanotubes have been used as probes in scanning probe microscopy. If the atomic placement and manipulation capability already demonstrated by scanning probe microscopy could be combined with a nanotube delivery system, a formidable nanoassembly tool would result. Here we report the achievement of controllable, reversible atomic scale mass transport along carbon nanotubes, using indium metal as the prototype transport species. This transport process has similarities to conventional electromigration, a phenomenon of critical importance to the semiconductor industry.