Autocatalytic chemical reactions, whereby a molecule is able to catalyze its own formation from a set of precursors, mimic nature's ability to generate identical copies of relevant biomolecules, and are thought to have been crucial for the origin of life. While several molecular autocatalysts have been previously reported, coupling autocatalytic behavior to macromolecular self-assembly has been challenging. Here, we report a non-enzymatic and chemoselective methodology capable of autocatalytically producing triskelion peptides that self-associate into spherical bioinspired nanostructures. Serial transfer experiments demonstrate that oligotriazole autocatalysis successfully leads to continual self-assembly of three-dimensional nanospheres. Triskelion-based spherical architectures offer an opportunity to organize biomolecules and chemical reactions in unique, nanoscale compartments. The use of peptide-based autocatalysts that are capable of self-assembly represents a promising method for the development of self-synthesizing biomaterials, and may shed light on understanding life's chemical origins.Molecules that act as both autocatalysts and material precursors offer exciting prospects for self-synthesizing materials. Here, the authors design a triazole peptide that self-replicates and then self-assembles into nanostructures, coupling autocatalytic and assembly pathways to realize a reproducing supramolecular system.