Nanosized inorganic particles are of great interest because their electronic properties can be easily tailored, providing a tremendous potential for applications in optoelectronic devices, light-emitting diodes, solar cells and hydrogen storage. Confinement of electrons and holes to dimensions comparable to their wavelength leads to quantum-well states with modified wavefunctions and density of states. Surface phenomena are crucial in determining nanoparticle properties in view of their large surface-to-volume ratio. Despite a wealth of information, many fundamental questions about the nature of the surface and its relationship with the electronic structure remain unsolved. Ab initio calculations on CdSe nanocrystals suggest that passivating the ligands does not produce the ideal wurtzite structure and that Se atoms relax outwards irrespective of passivation. Here we show that implanted positrons are trapped at the surface of CdSe nanocrystals. They annihilate mostly with the Se electrons, monitor changes in composition and structure of the surface while hardly sensing the ligand molecules, and we thus unambiguously confirm the predicted strong surface relaxation.