Single atoms and atomlike defects in solids are ideal quantum light sources and memories for quantum networks. However, most atomic transitions are in the ultraviolet-visible portion of the electromagnetic spectrum, where propagation losses in optical fibers are prohibitively large. Here, we observe for the first time the emission of single photons from a single Er^{3+} ion in a solid-state host, whose optical transition at 1.5  μm is in the telecom band, allowing for low-loss propagation in optical fiber. This is enabled by integrating Er^{3+} ions with silicon nanophotonic structures, which results in an enhancement of the photon emission rate by a factor of more than 650. Dozens of distinct ions can be addressed in a single device, and the splitting of the lines in a magnetic field confirms that the optical transitions are coupled to the electronic spin of the Er^{3+} ions. These results are a significant step towards long-distance quantum networks and deterministic quantum logic for photons based on a scalable silicon nanophotonics architecture.