Tau protein and its fragments self-assemble into amyloid fibrils in the presence of polyanions, such as heparin. By combining microscopy, scattering, and spectroscopy techniques, we studied the aggregation of the 26-mer Tau-derived peptide alone, Tau306-327, the third repeat fragment (R3) of the microtubule-binding domain. We show that: i) the sole Tau(306-327) can self-assemble into amyloid fibrils without the need of aggregation-promoting polyanions; ii) the resulting structures consist of surprisingly large, well-ordered 2D laminated flat ribbons, with a log-normal distribution of the lateral width, reaching the unprecedented lateral size of 350 nm and/or 45 individual protofilaments, that is, the largest amyloid laminated structures ever observed for Tau or any other amyloidogenic sequence. Our results provide insight into the molecular determinants of Tau aggregation and open new perspectives in the understanding of the assembly of amyloid fibrils and beta-sheet-based biomaterials.