Pegmatites are shallow, coarse-grained magmatic intrusions with crystals occasionally approaching meters in length. Compared to their plutonic hosts, pegmatites are thought to have cooled rapidly, suggesting that these large crystals must have grown fast. Growth rates and conditions, however, remain poorly constrained. Here we investigate quartz crystals and their trace element compositions from miarolitic cavities in the Stewart pegmatite in southern California, USA, to quantify crystal growth rates. Trace element concentrations deviate considerably from equilibrium and are best explained by kinetic effects associated with rapid crystal growth. Kinetic crystal growth theory is used to show that crystals accelerated from an initial growth rate of 10−6–10−7 m s−1 to 10−5–10−4 m s−1 (10-100 mm day−1 to 1–10 m day−1), indicating meter sized crystals could have formed within days, if these rates are sustained throughout pegmatite formation. The rapid growth rates require that quartz crystals grew from thin (micron scale) chemical boundary layers at the fluid-crystal interfaces. A strong advective component is required to sustain such thin boundary layers. Turbulent conditions (high Reynolds number) in these miarolitic cavities are shown to exist during crystallization, suggesting that volatile exsolution, crystallization, and cavity generation occur together.