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The anomalous abundances of sulfur isotopes in ancient sediments provide the strongest evidence for an anoxic atmosphere prior to ∼2.45 Ga, but the mechanism for producing this 'mass-independent' fractionation pattern remains in question. The prevailing hypothesis has been that it is created by differences in the UV photolysis rates of different SO2 isotopologues. We investigate here a recently proposed additional source of fractionation during gas-phase formation of elemental sulfur (S4 and S8). Because two minor S isotopes rarely occur in the same chain, the longer S4 and S8 chains should be strongly, and roughly equally, depleted in all minor isotopes. This gives rise to negative ∆(sup 33) S values and positive ∆(sub 36) S values in elemental sulfur-just the opposite of (and much larger than) what is predicted from SO2 photolysis itself. Back-reactions during chain formation, specifically photolysis of S2 and S3, pass sulfur having the opposite fractionation back to atomic S, and thence to other sulfur species, causing H2S, SO2, sulfate, and short-chain elemental sulfur to have positive ∆(sup 33) S and negative ∆(sup 36) S. Positive ∆(sup 33) S values in elemental sulfur produced in laboratory SO2 photolysis experiments could be caused by the initial fractionation during photolysis, combined with rapid condensation of short-chain sulfur species on the walls of the reaction chamber, along with a scarcity of back-reactions. The simulated fractionations produced by the chain formation mechanism do not directly match fractionations from the rock record. The mismatch might be explained if the isotopic signals leaving the atmosphere were significantly modulated by life, by uncertainties in the rates of reactions of both major and minor isotopic sulfur species, or by the relatively large potential range of atmospheric parameters. Further work is needed to better constrain these uncertainties, but this novel mechanism suggests new avenues to explore in our search for a explanation for the S-MIF record.