We investigate the structural properties and energy levels of simple intrinsic defects in gallium arsenide. The first-principles calculations (1) apply boundary conditions appropriate to charge defects in supercells and enable quantitatively accurate predictions of defect charge transitions with a supercell approximation, (2) are demonstrated to be converged with respect to cell size and (3) assess the sensitivity to model construction to Ga pseudopotential construction (3d core or 3d valence) and density functionals (local density or generalized gradient approximation). With these factors controlled, we present the first quantitatively reliable survey of defect levels in GaAs, reassess the available literature and begin to decipher the complexity of GaAs defect chemistry. The computed defect level spectrum spans the experimental GaAs band gap, defects exhibit multiple bistabilities with (sometimes overlapping) negative-U systems, express more extensive charge states than previously anticipated and collectively suggest that our atomistic understanding of GaAs defect physics needs to be reassessed.