To investigate the stability of various atomic arrangements of vacancy aggregates in GaAs, we make use of a self-consistent-charge density-functional-based tight-binding method. In contrast to silicon, where the corresponding number is 6, we find the first such stable aggregate to be made up of 12 vacancies. This is explained by the added possibility of energy lowering Ga-Ga and As-As dimer formation. Since these results are consistent with measured and calculated defect-related positron lifetimes, they give powerful evidence for the existence of such magic number vacancy aggregates in GaAs.