We use dynamical mass measurements of 16 black holes in transient low-mass X-ray binaries to infer the stellar black hole mass distribution in the parent population. We find that the observations are best described by a narrow mass distribution at 7.8 ± 1.2 M sun. We identify a selection effect related to the choice of targets for optical follow-ups that results in a flux-limited sample. We demonstrate, however, that this selection effect does not introduce a bias in the observed distribution and cannot explain the absence of black holes in the 2-5 M sun mass range. On the high-mass end, we argue that the rapid decline in the inferred distribution may be the result of the particular evolutionary channel followed by low-mass X-ray binaries. This is consistent with the presence of high-mass black holes in the persistent, high-mass X-ray binary sources. If the paucity of low-mass black holes is caused by a sudden decrease of the supernova explosion energy with increasing progenitor mass, this would have observable implications for ongoing transient surveys that target core-collapse supernovae. Our results also have significant implications for the calculation of event rates from the coalescence of black hole binaries for gravitational wave detectors.