The past decade has witnessed an explosion of techniques used to pattern polymers on the nano (1–100 nm) and submicrometre (100–1,000 nm) scale, driven by the extensive versatility of polymers for diverse applications, such as molecular electronics1, 2, data storage3, optoelectronics4, displays5, sacrificial templates6, 7 and all forms of sensors. Conceptually, most of the patterning techniques, including microcontact printing (soft lithography)8, photolithography9, 10, electron-beam lithography11, block-copolymer templating12, 13 and dip-pen lithography14, are based on the spatially selective removal or formation/deposition of polymer. Here, we demonstrate an alternative and novel lithography technique—electrostatic nanolithography using atomic force microscopy—that generates features by mass transport of polymer within an initially uniform, planar film without chemical crosslinking, substantial polymer degradation or ablation. The combination of localized softening of attolitres (102–105 nm3) of polymer by Joule heating, extremely non-uniform electric field gradients to polarize and manipulate the soften polymer, and single-step process methodology using conventional atomic force microscopy (AFM) equipment, establishes a new paradigm for polymer nanolithography, allowing rapid (of the order of milliseconds) creation of raised (or depressed) features without external heating of a polymer film or AFM tip–film contact.