Conventional lasers (from table-top systems to microscopic devices) typically operate in the so-called weak-coupling regime, involving large numbers of atoms and photons; individual quanta have a negligible impact on the system dynamics. However, this is no longer the case when the system approaches the regime of strong coupling for which the number of atoms and photons can become quite small. Indeed, the lasing properties of a single atom in a resonant cavity have been extensively investigated theoretically. Here we report the experimental realization of a one-atom laser operated in the regime of strong coupling. We exploit recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. The observed characteristics of the atom-cavity system are qualitatively different from those of the familiar many-atom case. Specifically, our measurements of the intracavity photon number versus pump intensity indicate that there is no threshold for lasing, and we infer that the output flux from the cavity mode exceeds that from atomic fluorescence by more than tenfold. Observations of the second-order intensity correlation function demonstrate that our one-atom laser generates manifestly quantum (nonclassical) light, typified by photon anti-bunching and sub-poissonian photon statistics.