Single atoms absorb and emit light from a resonant laser beam photon by photon. We show that a single atom strongly coupled to an optical cavity can absorb and emit resonant photons in pairs. The effect is observed in a photon correlation experiment on the light transmitted through the cavity. We find that the atom-cavity system transforms a random stream of input photons into a correlated stream of output photons, thereby acting as a two-photon gateway. The phenomenon has its origin in the quantum anharmonicity of the energy structure of the atom-cavity system. Future applications could include the controlled interaction of two photons by means of one atom.