Very rapid (<1 minute), high amplitude (>100) variability at >1e40 erg/s is nearly unprecedented in our Universe. We have recently discovered a new class of X-ray point sources showing such variability in two nearby galaxies while analyzing archival Chandra and XMM-Newton data. One source is located within a suspected globular cluster of the host galaxy and flared one time, while the other source is located in either a globular cluster of the host galaxy or the core of a stripped dwarf companion galaxy that flared on five occasions over a seven year time span. When not flaring, the sources appear as normal accreting neutron star or black hole X-ray binaries, indicating that the flare event does not significantly disrupt the system. We speculate on the nature of these explosive, yet non-destructive objects.