The production of amino acids and their condensation to polypeptides under plausibly prebiotic conditions have long been known. But despite the central importance of molecular self-replication in the origin of life, the feasibility of peptide self-replication has not been established experimentally. Here we report an example of a self-replicating peptide. We show that a 32-residue alpha-helical peptide based on the leucine-zipper domain of the yeast transcription factor GCN4 can act autocatalytically in templating its own synthesis by accelerating the thioester-promoted amide-bond condensation of 15- and 17-residue fragments in neutral, dilute aqueous solutions. The self-replication process displays parabolic growth pattern with the initial rates of product formation correlating with the square-foot of initial template concentration.