Applying square adsorption-well and Morse potential models for the adsorption of a sulfur specie on a solid surface, we have evaluated the fractionation of four sulfur isotopes (32S, 33S, 34S and 36S) during chemisorption reactions. Heterogeneous reactions between solid and aqueous (or gaseous) species are found to produce anomalous fractionations of sulfur isotopes when the adsorption energy is small (<0.3 eV; 30 kJ/mol) and a discontinuity occurs in the number of bound energy levels of different sulfur isotopes. We refer to “anomalous sulfur isotope fractionation” when the ∆33S and 33θ’ (≈δ33S/δ34S) values of a sample fall outside of 0±0.2‰ and 0.51±0.01‰, respectively, and/or when the ∆36S and 36θ’ (≈δ36S/δ34S) values of a sample fall outside of 0±0.4‰ and 1.9±0.1‰, respectively. The magnitude of anomalous sulfur isotope effects during a heterogeneous reaction increases with increasing temperature. Depending on the values of chemisorption energy and bond strength, the δ33S, δ34S, δ36S, Δ33S and Δ36S values of chemisorption products may be as variable as those observed in Archean sedimentary rocks.Ab initio calculations for SO2 adsorption on a kerogen surface indicate the possibility of creating anomalous isotope signatures for the adsorbed species, such as: δ33S/δ34S≈1.08, δ36S/δ34S≈0.84, Δ33S=7.0 to 13.6‰, and Δ36S=−13.0 to −25.2‰ in a temperature range of 0 to 200 °C; the magnitude of Δ33S and Δ36S increase with increasing temperature. These data, together with various geochemical data (e.g., organic C and sulfide S contents; hydrothermal alteration effects) on Archean sedimentary rocks with anomalous sulfur isotope fractionations, suggest that the anomalous sulfur isotope signatures in such rocks may have been created by heterogeneous reactions between organic matter (+ minerals) and sulfur-bearing aqueous solutions under hydrothermal conditions, rather than by UV photolysis of volcanic SO2 in an O2-poor atmosphere.