Additive manufacturing technologies based on layer-by-layer deposition of material ejected from a nozzle provide unmatched versatility but are limited in terms of printing speed and resolution. Electrohydrodynamic jetting uniquely allows generating submicrometer jets that can reach speeds above 1 m s-1, but such jets cannot be precisely collected by too slow mechanical stages. Here, we demonstrate that controlling the voltage applied to electrodes located around the jet, its trajectory can be continuously adjusted with lateral accelerations up to 106 m s-2. Through electrostatically deflecting the jet, 3D objects with submicrometer features can be printed by stacking nanofibers on top of each other at layer-by-layer frequencies as high as 2000 Hz. The fast jet speed and large layer-by-layer frequencies achieved translate into printing speeds up to 0.5 m s-1 in-plane and 0.4 mm s-1 in the vertical direction, three to four orders of magnitude faster than techniques providing equivalent feature sizes.