We report the first observation of photon antibunching in the photoluminescence from single carbon nanotubes. The emergence of a fast luminescence decay component under strong optical excitation indicates that Auger processes are partially responsible for inhibiting two-photon generation. Additionally, the presence of exciton localization at low temperatures ensures that nanotubes emit photons predominantly one by one. The fact that multiphoton emission probability can be smaller than 5% suggests that carbon nanotubes could be used as a source of single photons for applications in quantum cryptography.