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Mass-independent fractionation (MIF) of sulfur isotopes has been reported in sediments of Archean and Early Proterozoic Age (>2.3 Ga) but not in younger rocks. The only fractionation mechanism that is consistent with the data on all four sulfur isotopes involves atmospheric photochemical reactions such as SO₂ photolysis. We have used a one-dimensional photochemical model to investigate how the isotopic fractionation produced during SO₂ photolysis would have been transferred to other gaseous and particulate sulfur-bearing species in both low-O₂ and high-O₂ atmospheres. We show that in atmospheres with O₂ concentrations <10^-5 times the present atmospheric level (PAL), sulfur would have been removed from the atmosphere in a variety of different oxidation states, each of which would have had its own distinct isotopic signature. By contrast, in atmospheres with O₂ concentrations ≥10^-5 PAL, all sulfur-bearing species would have passed through the oceanic sulfate reservoir before being incorporated into sediments, so any signature of MIF would have been lost. We conclude that the atmospheric O₂ concentration must have been <10^-5 PAL prior to 2.3 Ga.