The imaging of dynamical processes at interfaces and on the nanoscale is of great importance throughout science and technology. While light-optical imaging techniques often cannot provide the necessary spatial resolution, electron-optical techniques damage the specimen and cause dose-induced artifacts. Here, optical near-field electron microscopy (ONEM) is proposed, an imaging technique that combines noninvasive probing with light, with a high-spatial-resolution readout via electron optics. Close to the specimen, the optical near fields are converted into a spatially varying electron flux using a planar photocathode. The electron flux is imaged using low-energy electron microscopy, enabling label-free nanometric resolution without the need to scan a probe across the sample. The specimen is never exposed to damaging electrons.