Misfolding of the microtubule-binding protein tau into filamentous aggregates is characteristic of many neurodegenerative diseases such as Alzheimer's disease and progressive supranuclear palsy. Determining the structures and dynamics of these tau fibrils is important for designing inhibitors against tau aggregation. Tau fibrils obtained from patient brains have been found by cryo-electron microscopy to adopt disease-specific molecular conformations. However, in vitro heparin-fibrillized 2N4R tau, which contains all four microtubule-binding repeats (4R), was recently found to adopt polymorphic structures. Here we use solid-state NMR spectroscopy to investigate the global fold and dynamics of heparin-fibrillized 0N4R tau. A single set of ¹³C and ¹⁵N chemical shifts was observed for residues in the four repeats, indicating a single β-sheet conformation for the fibril core. This rigid core spans the R2 and R3 repeats and adopts a hairpin-like fold that has similarities to but also clear differences from any of the polymorphic 2N4R folds. Obtaining a homogeneous fibril sample required careful purification of the protein and removal of any proteolytic fragments. A variety of experiments and polarization transfer from water and mobile side chains indicate that 0N4R tau fibrils exhibit heterogeneous dynamics: Outside the rigid R2-R3 core, the R1 and R4 repeats are semirigid even though they exhibit β-strand character and the proline-rich domains undergo large-amplitude anisotropic motions, whereas the two termini are nearly isotropically flexible. These results have significant implications for the structure and dynamics of 4R tau fibrils in vivo.