The protein α-synuclein is the main component of Lewy bodies, the neuron-associated aggregates seen in Parkinson disease and other neurodegenerative pathologies. An 11-residue segment, which we term NACore, appears to be responsible for amyloid formation and cytotoxicity of human α-synuclein. Here we describe crystals of NACore that have dimensions smaller than the wavelength of visible light and thus are invisible by optical microscopy. As the crystals are thousands of times too small for structure determination by synchrotron X-ray diffraction, we use micro-electron diffraction to determine the structure at atomic resolution. The 1.4 Å resolution structure demonstrates that this method can determine previously unknown protein structures and here yields, to our knowledge, the highest resolution achieved by any cryo-electron microscopy method to date. The structure exhibits protofibrils built of pairs of face-to-face β-sheets. X-ray fibre diffraction patterns show the similarity of NACore to toxic fibrils of full-length α-synuclein. The NACore structure, together with that of a second segment, inspires a model for most of the ordered portion of the toxic, full-length α-synuclein fibril, presenting opportunities for the design of inhibitors of α-synuclein fibrils.