The properties of magnetic nanoparticles tend to be depressed by the unavoidable presence of a magnetically inactive surface layer. However, outstanding magnetic properties with a room-temperature magnetization near the bulk value can be produced by high-temperature synthesis methods involving capping with organic acid. The capping molecules are not magnetic, so the origin of the enhanced magnetization remains elusive. In this work, we present a real-space characterization on the subnanometer scale of the magnetic, chemical, and structural properties of iron-oxide nanoparticles via aberration-corrected scanning transmission electron microscopy. For the first time, electron magnetic chiral dichroism is used to map the magnetization of nanoparticles in real space with subnanometer spatial resolution. We find that the surface of the nanoparticles is magnetically ordered. Combining the results with density functional calculations, we establish how magnetization is restored in the surface layer. The bonding with the acid's O atoms results in O-Fe atomic configuration and distances close to bulk values. We conclude that the nature and number of molecules in the capping layer is an essential ingredient in the fabrication of nanoparticles with optimal magnetic properties.