Pearls, the most flawless and highly prized of them, are perhaps the most perfectly spherical macroscopic bodies in the biological world. How are they so round? Why are other pearls solids of revolution (off-round, drop, ringed), and yet others have no symmetry (baroque)? We find that with a spherical pearl the growth fronts of nacre are spirals and target patterns distributed across its surface, and this is true for a baroque pearl, too, but that in pearls with rotational symmetry spirals and target patterns are found only in the vicinity of the poles; elsewhere the growth fronts are arrayed in ratchet fashion around the equator. We demonstrate that pearl rotation is a self-organized phenomenon caused and sustained by physical forces from the growth fronts, and that rotating pearls are a - perhaps unique - example of a natural ratchet.