We report a study of a defect responsible for the ‘‘g’’ bound exciton line at 1.5112eV that is frequently detected in photoluminescence spectra of GaAs grown by molecular beam epitaxy (MBE). A direct correlation has been observed between this line and a transition at 1.4946eV, which is shown to result from a conduction band‐to‐acceptor recombination involving a shallow, unidentified acceptorlike defect that is labeled ‘‘A.’’ The activation energy of the defect is 24.8±0.2 meV, about 1.7 meV lower than that of CAsacceptor. Upon hydrogenation the defect is passivated more extensively than any known shallow acceptor species in GaAs. This result is analyzed in terms of a passivation model, from which it can be inferred that the A defect is not due to a simple substitutional Group II impurity on a Ga site. Incorporation of the A defect strongly affects the luminescence properties of the material. An almost complete quenching of the donor‐bound exciton lines, profound changes in the line shape and relative intensity of the free exciton recombination, and appearance of a sharp transition of unknown origin at 1.5138eV were observed with increasing defect concentration. Apparently ‘‘donorless’’ low temperature exciton recombination spectra are reported for defect‐richp‐type MBE GaAs layers with donor concentrations as high as 7×1014cm−3and compensation ratios of ∼0.3. The dependence of the defect incorporation on MBE growth parameters is discussed. The feasibility of MBE growth of high purity, nearly shallow defect‐freep‐type GaAs layers at marginally As‐stabilized surface conditions over an about 1–5 &mgr;m/h range of deposition rates is demonstrated.