Red abalone (Haliotis rufescens) nacre is a layered composite biomineral that contains crystalline aragonite tablets confined by organic layers. Nacre is intensely studied because its biologically controlled microarchitecture gives rise to remarkable strength and toughness, but the mechanisms leading to its formation are not well understood. Here we present synchrotron spectromicroscopy experiments revealing that stacks of aragonite tablet crystals in nacre are misoriented with respect to each other. Quantitative measurements of crystal orientation, tablet size, and tablet stacking direction show that orientational ordering occurs not abruptly but gradually over a distance of 50 microm. Several lines of evidence indicate that different crystal orientations imply different tablet growth rates during nacre formation. A theoretical model based on kinetic and gradual selection of the fastest growth rates produces results in qualitative and quantitative agreement with the experimental data and therefore demonstrates that ordering in nacre is a result of crystal growth kinetics and competition either in addition or to the exclusion of templation by acidic proteins as previously assumed. As in other natural evolving kinetic systems, selection of the fastest-growing stacks of tablets occurs gradually in space and time. These results suggest that the self-ordering of the mineral phase, which may occur completely independently of biological or organic-molecule control, is fundamental in nacre formation.