The source of sulfur in giant Norilsk-type sulfide deposits is discussed. A review of the state of the problem and a critical analysis of existing hypotheses are made. The distribution of δ34S in sulfides of ore occurrences and small and large deposits and in normal sedimentary, metamorphogenic, and hypogene sulfates is considered. A large number of new δ34S data for sulfides and sulfates in various deposits, volcanic and terrigenous rocks, coals, graphites, and metasomatites are presented. The main attention is focused on the objects of the Norilsk and Kureika ore districts. The δ34S value varies from –14 to + 22.5‰ in sulfides of rocks and ores and from 15.3 to 33‰ in anhydrites. In sulfide–sulfate intergrowths and assemblages, δ34S is within 4.2–14.6‰ in sulfides and within 15.3–21.3‰ in anhydrites. The most isotopically heavy sulfur was found in pyrrhotite veins in basalts (δ34S = 21.6‰), in sulfate veins cutting dolomites (δ34S = 33‰), and in subsidence caldera sulfates in basalts (δ34S = 23.2–25.2‰). Sulfide ores of the Tsentral’naya Shilki intrusion have a heavy sulfur isotope composition (δ34S = + 17.7‰ (n = 15)). Thermobarogeochemical studies of anhydrites have revealed inclusions of different types with homogenization temperatures ranging from 685 °C to 80 °C. Metamorphogenic and hypogene anhydrites are associated with a carbonaceous substance, and hypogene anhydrites have inclusions of chloride-containing salt melts. We assume that sulfur in the trap sulfide deposits was introduced with sulfates of sedimentary rocks (δ34S = 22–24‰). No assimilation of sulfates by basaltic melt took place. The sedimentary anhydrites were “steamed” by hydrocarbons, which led to sulfate reduction and δ34S fractionation. As a result, isotopically light sulfur accumulated in sulfides and hydrogen sulfide, isotopically heavy sulfur was removed by aqueous calcium sulfate solution, and “residual” metamorphogenic anhydrite acquired a lighter sulfur isotope composition as compared with the sedimentary one. The wide variations in δ34S in sulfides and sulfates are due to changes in the physicochemical parameters of the ore-forming system (first of all, temperature and PCH4) during the sulfate reduction. The regional hydrocarbon resources were sufficient for large-scale ore formation.