Optical nonlinearities typically require macroscopic media, thereby making their implementation at the quantum level an outstanding challenge. Here, we demonstrate a nonlinearity for one atom enclosed by two highly reflecting mirrors. We send laser light through the input mirror and record the light from the output mirror of the cavity. For weak laser intensity, we find the vacuum-Rabi resonances. But for higher intensities, we observe an extra resonance, which originates from the fact that the cavity can accommodate only an integer number of photons and that this photon number determines the characteristic frequencies of the coupled atom-cavity system. We selectively excite such a frequency by depositing two photons at once into the system and find a transmission that increases with the laser intensity squared. The nonlinearity differs from classical saturation nonlinearities and is direct spectroscopic proof of the quantum nature of the atom-cavity system. It provides a photon-photon interaction by means of one atom, and constitutes a step towards a two-photon gateway or a single-photon transistor.