The static structure factor S(q) for a dispersion of charged colloidal particles is obtained for large values of the wavevector q by a model of the one-component plasma (OCP) in which the direct correlation function c(r) is known analytically. The model OCP is then used as a reference system for a perturbation theory of the small q behavior of the structure factor based upon a form of the random phase approximation suitably modified to treat the inclusion of a hard core in the perturbation potential. Explicit results are obtained for the coefficients in a small q expansion of the Fourier transform of the direct correlation function c(q). The values of S(q=0) determined from the extrapolation of the experimental data are analyzed in terms of the screened Coulomb interaction from the DLVO theory of colloid stability. The calculated surface potentials are found to be smaller than the values normally associated with this type of system. The theory gives the correct qualitative form for the small q region of S(q) in dense dispersions near the melting transition. At lower particle densities, the theory predicts the existence of a shallow minimum in S(q) at small q.