From our earlier studies, it comes out that proteinogenic amino acids undergo spontaneous oscillatory chiral conversion and condensation. An understanding of these phenomena is crucial in view of the fact that amino acids are the building blocks of proteins and peptides present in all living organisms. Moreover, amino acids play an increasingly important role as components of drugs, dietary supplements, and cosmetics. In this study, we trace spontaneous oscillatory reactions of L-methionine (L-Met) with use of thin-layer chromatography with densitometric and mass spectrometric detection, and high-performance liquid chromatography with evaporative light scattering detection. Additional measurements were carried out with use of scanning electron microscopy. The results obtained confirm that L-Met spontaneously undergoes chiral conversion and peptidization. As an outcome of these two processes, peptides are formed of considerably different chemical structures, able to self-organize in nano- and microstructures under the mild ambient conditions without any catalysts.