Tunneling transport measurements performed on single particles and on arrays of Fe3O4 (magnetite) nanocrystals provide strong evidence for the existence of the Verwey metal-insulator transition at the nanoscale. The resistance measurements on nanocrystal arrays show an abrupt increase of the resistance around 100 K, consistent with the Verwey transition, while the current-voltage characteristics exhibit a sharp transition from an insulator gap to a peak structure around zero bias voltage. The tunneling spectra obtained on isolated particles using a Scanning Tunneling Microscope reveal an insulator-like gap structure in the density of states below the transition temperature that gradually disappeared with increasing temperature, transforming to a small peak structure at the Fermi energy. These data provide insight into the roles played by long- and short-range charge ordering in the Verwey transition.