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The consequences of global warming for fisheries are not well understood, but the geological record demonstrates that carbon cycle perturbations are frequently associated with ocean deoxygenation. Of particular interest is the Paleocene-Eocene Thermal Maximum (PETM), where the carbon dioxide input into the atmosphere was similar to the IPCC RCP8.5 emission scenario. Here we present sulfur-isotope data that record a positive 1 per mil excursion during the PETM. Modeling suggests that large parts of the ocean must have become sulfidic. The toxicity of hydrogen sulfide will render two of the largest and least explored ecosystems on Earth, the mesopelagic and bathypelagic zones, uninhabitable by multicellular organisms. This will affect many marine species whose ecozones stretch into the deep ocean.