The Moon is currently locked in a spin-orbit resonance of synchronous rotation, of which one consequence is that more impacts should occur near the Moon's apex of motion (0 degrees N, 90 degrees W) than near its antapex of motion (0 degrees N, 90 degrees E). Several of the largest lunar impact basins could have temporarily unlocked the Moon from synchronous rotation, and after the re-establishment of this state the Moon would have been left in either its initial orientation, or one that was rotated 180 degrees about its spin axis. We show that there is less than a 2% probability that the oldest lunar impact basins are randomly distributed across the lunar surface. Furthermore, these basins are preferentially located near the Moon's antapex of motion, and this configuration has less than a 0.3% probability of occurring by chance. We postulate that the current near side of the Moon was in fact its far side when the oldest basins formed. One basin with the required size and temporal characteristics to account for a 180 degrees reorientation is the Smythii basin.