Chemical evolution of planetary bodies, ranging from asteroids to the large rocky planets, is thought to begin with differentiation through solidification of magma oceans many hundreds of kilometres in depth. The Earth's Moon is the archetypical example of this type of differentiation. Evidence for a lunar magma ocean is derived largely from the widespread distribution, compositional and mineralogical characteristics, and ancient ages inferred for the ferroan anorthosite (FAN) suite of lunar crustal rocks. The FANs are considered to be primary lunar flotation-cumulate crust that crystallized in the latter stages of magma ocean solidification. According to this theory, FANs represent the oldest lunar crustal rock type. Attempts to date this rock suite have yielded ambiguous results, however, because individual isochron measurements are typically incompatible with the geochemical make-up of the samples, and have not been confirmed by additional isotopic systems. By making improvements to the standard isotopic techniques, we report here the age of crystallization of FAN 60025 using the (207)Pb-(206)Pb, (147)Sm-(143)Nd and (146)Sm-(142)Nd isotopic systems to be 4,360 ± 3 million years. This extraordinarily young age requires that either the Moon solidified significantly later than most previous estimates or the long-held assumption that FANs are flotation cumulates of a primordial magma ocean is incorrect. If the latter is correct, then much of the lunar crust may have been produced by non-magma-ocean processes, such as serial magmatism.