We demonstrate the generation of triggered single photons at a predetermined and well defined energy using the radiative recombination of single nitrogen-bound excitons in a semiconductor. The nitrogen atoms are embedded in a ZnSe quantum well structure and were excited by nonresonant optical pumping (82 MHz) at low temperature (4 K). We find resolution-limited photoluminescence lines (280 micro eV) which display photon antibunching under continuous optical pumping. Our results also suggest that single nitrogen-bound excitons are well suited for cavity quantum electrodynamics experiments.