Amyloid fibrils are self-assembled filamentous structures associated with protein deposition conditions including Alzheimer's disease and the transmissible spongiform encephalopathies. Despite the immense medical importance of amyloid fibrils, no atomic-resolution structures are available for these materials, because the intact fibrils are insoluble and do not form diffraction-quality 3D crystals. Here we report the high-resolution structure of a peptide fragment of the amyloidogenic protein transthyretin, TTR(105-115), in its fibrillar form, determined by magic angle spinning NMR spectroscopy. The structure resolves not only the backbone fold but also the precise conformation of the side chains. Nearly complete 13 C and 15 N resonance assignments for TTR(105-115) formed the basis for the extraction of a set of distance and dihedral angle restraints. A total of 76 self-consistent experimental measurements, including 41 restraints on 19 backbone dihedral angles and 35 13 C-15 N distances between 3 and 6 Å were obtained from 2D and 3D NMR spectra recorded on three fibril samples uniformly 13 C, 15 N-labeled in consecutive stretches of four amino acids and used to calculate an ensemble of peptide structures. Our results indicate that TTR(105-115) adopts an extended -strand conformation in the amyloid fibrils such that both the main-and side-chain torsion angles are close to their optimal values. Moreover, the structure of this peptide in the fibrillar form has a degree of long-range order that is generally associated only with crystalline materials. These findings provide an explanation of the unusual stability and characteristic properties of this form of polypeptide assembly.