Since the realization that the tips of scanning probe microscopes can interact with atoms at surfaces, there has been much interest in the possibility of building or modifying nanostructures or molecules directly from single atoms(1). Individual large molecules can be positioned on surfaces(2-4), and atoms can be transferred controllably between the sample and probe tip(5,6). The most complex structures(7-11) are produced at cryogenic temperatures by sliding atoms across a surface to chosen sites. But there are problems in manipulating atoms laterally at higher temperatures-atoms that are sufficiently well bound to a surface to be stable at higher temperatures require a stronger tip interaction to be moved. This situation differs significantly from the idealized weakly interacting tips(12,13) of scanning tunnelling or atomic force microscopes. Here we demonstrate that precise positioning of atoms on a copper surface is possible at room temperature. The triggering mechanism for the atomic motion unexpectedly depends on the tunnelling current density, rather than the electric field or proximity of tip and surface.