One of the oldest open questions in semiconductor physics is the origin of the small splittings of the neutral acceptor ground state in silicon which lead to a distribution of doublet splittings rather than the fourfold-degenerate state of Gamma(8) symmetry expected in the absence of perturbations. Here we show that these acceptor ground state splittings are absent in the photoluminescence spectra of acceptor bound excitons in isotopically purified 28Si, demonstrating conclusively the surprising result that the splittings previously observed in natural Si result from the randomness of the Si isotopic composition.