Amyloid fibrils are implicated in over 20 neurodegenerative diseases. The mechanisms of fibril structuring and formation are not only of medical and biological importance but are also relevant for material science and nanotechnologies due to the unique structural and physical properties of amyloids. We previously found that hen egg white lysozyme, homologous to the disease-related human lysozyme, can form left-handed giant ribbons, closing into nanotubes. By using matrix-assisted laser desorption ionization mass spectrometry analysis, we here identify a key component of such structures: the ILQINS hexapeptide. By combining atomic force microscopy and circular dichorism, we find that this fragment, synthesized by solid-phase peptide synthesis, also forms fibrillar structures in water at pH 2. However, all fibrillar structures formed possess an unexpected right-handed twist, a rare chirality within the corpus of amyloid experimental observations. We confirm by small- and wide-angle X-ray scattering and molecular dynamics simulations that these fibrils are composed of conventional left-handed β-sheets, but that packing stresses between adjacent sheets create this twist of unusual handedness. We also show that the right-handed fibrils represent a metastable state toward β-sheet-based microcrystals formation.