We have demonstrated efficient production of triggered single photons by coupling a single semiconductor quantum dot to a three-dimensionally confined optical mode in a micropost microcavity. The efficiency of emitting single photons into a single-mode traveling wave is approximately 38%, which is nearly 2 orders of magnitude higher than for a quantum dot in bulk semiconductor material. At the same time, the probability of having more than one photon in a given pulse is reduced by a factor of 7 as compared to light with Poissonian photon statistics.