The opposition effect, the sharp surge in brightness of an astronomical object observed near zero phase angle, which has been known for more than a century, has generally been explained by shadow hiding. The reflectances of several Apollo lunar soil samples have been measured as a function of phase angle in linearly and circularly polarized light. All samples exhibited a decrease in the linear polarization ratio and an increase in the circular polarization ratio in the opposition peak. This provides unequivocal proof that most of the lunar opposition effect is caused by coherent backscatter, not shadow hiding. This result has major implications for the interpretation of photometric observations of bodies in the solar system, including the Earth.