During five years of Chandra observations, we have identified seven X-ray transients located within 23 pc of \sgrastar. These sources each vary in luminosity by more than a factor of 10, and have peak X-ray luminosities greater than 5 * 1033 \ergs, which strongly suggests that they are accreting black holes or neutron stars. The peak luminosities of the transients are intermediate between those typically considered outburst and quiescence for X-ray binaries. Remarkably four of these transients lie within only 1 pc of \sgrastar. This implies that, compared to the numbers of similar systems located between 1 and 23 pc, transients are over-abundant by a factor of 20 per unit stellar mass within 1 pc of \sgrastar. It is likely that the excess transient X-ray sources are low-mass X-ray binaries that were produced, as in the cores of globular clusters, by three-body interactions between binary star systems and either black holes or neutron stars that have been concentrated in the central parsec through dynamical friction. Alternatively, they could be high-mass X-ray binaries that formed among the young stars that are present in the central parsec.