We present a first-principles study of positron trapping at a negatively charged As vacancy in GaAs. Lattice relaxations induced both by the presence of the defect and of the positron have been included in a self-consistent way. In the presence of a positron, the volume of the vacancy increases and its symmetry is lowered. The positron wave function is well localized in the defect. Calculated positron lifetime and angular correlations of annihilation photons are in good agreement with recent experiments.