Full configuration interaction (FCI) calculations are useful as benchmarks for approximate techniques used in quantum chemistry : they are indeed the desired goal for all energy and wave function calculations in that they are the best solution to the Schrodinger equation within a finite basis Ansatz. Application of the method is limited due to the rapid increase in the number of configurations as the basis set size is increased. Many means have been applied to limit the number of terms in the expansion with the best known method being the singles and doubles expansion CI(SD), A Monte Carlo algorithm is proposed here whereby a CI expansion is allowed to expand by randomly including new terms which interact with those terms already present in the expansion. Solution of the variational problem is then performed for these randomly chosen configurations and a selection criterium for the resulting CI coefficients is applied. Repeated application of this method allows for estimates of the FCI energy. Calculations for the water molecule are performed to demonstrate the method.