Second harmonic generation in CdSe nanocrystal quantum dots is observed by Hyper-Rayleigh scattering. The size dependence of the first hyperpolarizibility β was investigated for the nanocrystals in solution. The value of β per nanocrystal decreases with size down to approximately 13 Å in radius. An increase is observed with further size reduction. The unit cell normalized second harmonic coefficient, β, shows a substantial systematic enhancement in small diameters. The observed size dependence of the second harmonic generation is explained assuming two contributions. The first is a bulklike contribution, from the noncentrosymmetric nanocrystal core, and the second, a contribution from the nanocrystal surface. The latter contribution is most significant in small nanocrystals with a substantial proportion of surface atoms. This result suggests that the second harmonic generation technique may be used as a probe of nanocrystal surfaces, in analogy to its common use as a probe of bulk surfaces.