Recent advances in nanotechnologies have prompted the need for tools to accurately and non-invasively manipulate individual nano-objects. Among the possible strategies, optical forces have been predicted to provide researchers with nano-optical tweezers capable of trapping a specimen and moving it in three dimensions. In practice, however, the combination of weak optical forces and photothermal issues has thus far prevented their experimental realization. Here, we demonstrate the first three-dimensional optical manipulation of single 50 nm dielectric objects with near-field nanotweezers. The nano-optical trap is built by engineering a bowtie plasmonic aperture at the extremity of a tapered metal-coated optical fibre. Both the trapping operation and monitoring are performed through the optical fibre, making these nanotweezers totally autonomous and free of bulky optical elements. The achieved trapping performances allow for the trapped specimen to be moved over tens of micrometres over a period of several minutes with very low in-trap intensities. This non-invasive approach is foreseen to open new horizons in nanosciences by offering an unprecedented level of control of nanosized objects, including heat-sensitive biospecimens.