The generation of non-classical states of light is of fundamental scientific and technological interest. For example, 'squeezed' states enable measurements to be performed at lower noise levels than possible using classical light. Deterministic (or triggered) single-photon sources exhibit non-classical behaviour in that they emit, with a high degree of certainty, just one photon at a user-specified time. (In contrast, a classical source such as an attenuated pulsed laser emits photons according to Poisson statistics.) A deterministic source of single photons could find applications in quantum information processing, quantum cryptography and certain quantum computation problems. Here we realize a controllable source of single photons using optical pumping of a single molecule in a solid. Triggered single photons are produced at a high rate, whereas the probability of simultaneous emission of two photons is nearly zero--a useful property for secure quantum cryptography. Our approach is characterized by simplicity, room temperature operation and improved performance compared to other triggered sources of single photons.