The properties of iron-based superconductors (Fe-SCs) can be varied dramatically with the introduction of dopants and atomic defects. As a pressing example, FeSe, parent phase of the highest-T-c Fe-SC, exhibits prevalent defects with atomic-scale ``dumbbell'' signatures as imaged by scanning tunneling microscopy (STM). These defects spoil superconductivity when their concentration exceeds 2.5%. Resolving their chemical identity is a prerequisite to applications such as nanoscale patterning of superconducting/nonsuperconducting regions in FeSe as well as fundamental questions such as the mechanism of superconductivity and the path by which the defects destroy it. We use STM and density functional theory to characterize and identify the dumbbell defects. In contrast to previous speculations about Se adsorbates or substitutions, we find that an Fe-site vacancy is the most energetically favorable defect in Se-rich conditions and reproduces our observed STM signature. Our calculations shed light more generally on the nature of Se capping, the removal of Fe vacancies via annealing, and their ordering into a root 5 x root 5 superstructure in FeSe and related alkali-doped compounds.