Second Harmonic Generation in CdSe nanocrystal quantum dots is observed by Hyper-Rayleigh scattering. We use a Ti-Sapphire femtosecond laser at 820 nm to induce the nonlinear optical response of the nanocrystals in solution. The unit cell normalized second harmonic coefficient β n, shows a substantial systematic enhancement in small sizes. The observed size dependence of the second harmonic generation process, is explained assuming two contributions. The first is a bulk-like contribution, from the non-centrosymmetric nanocrystal core, and the second, a contribution from the particle surface. The latter contribution is most significant in small nanocrystals with a substantial proportion of surface atoms.