Wear of sliding contacts leads to energy dissipation and device failure, resulting in massive economic and environmental costs(1). Typically, wear phenomena are described empirically(2), because physical and chemical interactions at sliding interfaces are not fully understood at any length scale. Fundamental insights from individual nanoscale contacts are crucial for understanding wear at larger length scales(3), and to enable reliable nanoscale devices, manufacturing and microscopy(4-6). Observable nanoscale wear mechanisms include fracture and plastic deformation(8) but recent experiments(9-11) and models(12) propose another mechanism: wear via atom-by-atom removal ('atomic attrition'), which can be modelled using stress-assisted chemical reaction kinetics(13). Experimental evidence for this has so far been inferential. Here, we quantitatively measure the wear of silicon a material relevant to small-scale devices(14) using in situ transmission electron microscopy. We resolve worn volumes as small as 25 +/- 5 nm(3), a factor of 10(3) lower than is achievable using alternative techniques(15,16). Wear of silicon against diamond is consistent with atomic attrition, and inconsistent with fracture or plastic deformation, as shown using direct imaging. The rate of atom removal depends exponentially on stress in the contact, as predicted by chemical rate kinetics(13). Measured activation parameters are consistent with an atom-by-atom process(17). These results, by direct observation, establish atomic attrition as the primary wear mechanism of silicon in vacuum at low loads.