Fibrils and oligomers are the aggregated protein agents of neuronal dysfunction in ALS diseases. Whereas we now know much about fibril architecture, atomic structures of disease-related oligomers have eluded determination. Here, we determine the corkscrew-like structure of a cytotoxic segment of superoxide dismutase 1 (SOD1) in its oligomeric state. Mutations that prevent formation of this structure eliminate cytotoxicity of the segment in isolation as well as cytotoxicity of the ALS-linked mutants of SOD1 in primary motor neurons and in a Danio rerio (zebrafish) model of ALS. Cytotoxicity assays suggest that toxicity is a property of soluble oligomers, and not large insoluble aggregates. Our work adds to evidence that the toxic oligomeric entities in protein aggregation diseases contain antiparallel, out-of-register β-sheet structures and identifies a target for structure-based therapeutics in ALS.