We have performed stress-dependent photoluminescence measurements on excitons bound to neutral shallow acceptors (A0X) in GaAs. From their temperature and stress variation three lines (at zero stress) are proved to be due to the decay of (A0X) with the J=52 state lowest. When low uniaxial stress (0-2 kg mm -2) is applied these three lines split into 7 or 8 components, although at high stress only one line remains with a stress shift equal to that for the conduction band to acceptor recombination. A theoretical interpretation based on a bonding two-hole state analogous to the H2 molecule is found to agree well with the data when the effects of a weak crystal field are included. Small deviations between this theory and experiment are presumed to indicate the importance of the antibonding two-hole functions in the (A0X) wave function. © 1975 The American Physical Society.