The de Broglie wave nature of matter is a paradigmatic example of quantum physics and it has been exploited in precision measurements of forces and fundamental constants. However, matter-wave interferometry has remained an outstanding challenge for natural polypeptides, building blocks of life, which are fragile and difficult to handle. Here, we demonstrate the wave nature of gramicidin, a natural antibiotic composed of 15 amino acids. Its center of mass is delocalized over more than 20 times the molecular size in our time-domain Talbot-Lau interferometer. We compare the observed interference fringes with a model that includes both a rigorous treatment of the peptide’s quantum wave nature as well as a quantum chemical assessment of its optical properties to distinguish our result from classical predictions. The realization of quantum optics with this prototypical biomolecule paves the way for quantum-assisted measurements on a large class of biologically relevant molecules.