It is proposed that lunar crustal asymmetries are the result of convective processes acting early in the Moon's history, during the magma-ocean phase and after synchronous rotation was established. Buoyant anorthositic crystals were transported to the farside by a large-scale circulation, called tilted convection, known to occur spontaneously in chaotic convective systems. The circulation was oriented toward the farside of the Moon by a small temperature contrast produced by radiative thermal shielding due to the proximity of Earth. Crustal thickening near the equator resulted from the modification of tilted convection by the Coriolis force. The anorthosite that was transported to the farside and equator may be a major cause of the observed crustal asymmetries and of the associated offset of the center of figure from the center of mass and bimodal hyposgram. The selective transport may have resulted in a nearside excess of incompatible elements, leading to the formation of the Procellarium KREEP terrane.