Colloidal chemistry techniques were used to synthesize ZnO particles in the nanometer size regime. The particle aging kinetics were determined by monitoring the optical band edge absorption and using the effective mass model to approximate the particle size as a function of time. We show that the growth kinetics of the ZnO particles follow the Lifshitz-Slyozov-Wagner theory for Ostwald ripening. In this model, the higher curvature and hence chemical potential of smaller particles provides a driving force for dissolution. The larger particles continue to grow by diffusion-limited transport of species dissolved in solution.