Harnessing nonlinearities strong enough to allow single photons to interact with one another is not only a fascinating challenge but also central to numerous advanced applications in quantum information science. Here we report the nonlinear interaction between two single photons. Each photon is generated in independent parametric down-conversion sources. They are subsequently combined in a nonlinear waveguide where they are converted into a single photon of higher energy by the process of sum-frequency generation. Our approach results in the direct generation of photon triplets. More generally, it highlights the potential for quantum nonlinear optics with integrated devices and, as the photons are at telecom wavelengths, it opens the way towards novel applications in quantum communication such as device-independent quantum key distribution.