Understanding the origin of defects in lead halide perovskite nanocrystals is paramount to attaining long-term structural stability and improved optical efficiency, key features for their successful implementation in optoelectronic devices. Unlike other studies, we explore the possible formation of trap states in explicit, nonperiodic CsPbBr3 nanocrystal models about 3 nm in size. Using density functional theory, we compute the defect formation energies of interstitial, vacancy, and antisite defects in different regions of the nanocrystal (center, surface center, and surface edge), demonstrating that the most stable defect position is found at the surface. We ascribe the high defect tolerance of CsPbBr3 nanocrystals to the fact that vacancies, i.e. the loss of surface ligands as ion pairs, are energetically difficult to form and only excessive stripping of surface ligands might be problematic, as their detachment leaves undercoordinated Br- on the crystal surface that only in this case translates into deep traps.