The kinetics of a first-order, solid-solid phase transition were investigated in the prototypical nanocrystal system CdSe as a function of crystallite size. In contrast to extended solids, nanocrystals convert from one structure to another by single nucleation events, and the transformations obey simple unimolecular kinetics. Barrier heights were observed to increase with increasing nanocrystal size, although they also depend on the nature of the nanocrystal surface. These results are analogous to magnetic phase transitions in nanocrystals and suggest general rules that may be of use in the discovery of new metastable phases.