The magnitude of the energy gap in nuclear matter associated with a highly correlated ground state of of the type believed to be important in the theory of superconductivity has been evaluated theoretically. The integral equation of Cooper, Mills, and Sessler is linearized and transformed into a form suitable for numerical solution. The energy gap, calculated by using an appropriate single-particle potential and the Gammel-Thaler two-body potential, is found to be a very strong function of the density of nuclear matter, and of the effective mass at the Fermi surface. It is concluded that the magnitude of the energy gap for nuclear matter should not be compared directly with experimental values for finite nuclei, although the results suggest that if the theory is extended to apply to finite nuclei it probably would be in agreement with experiment.