An exact solution of the mean spherical approximation for charged hard spheres in a neutralizing background is used to calculate various static properties of the classical one-component plasma in the strong coupling regime. The expressions involved are simple and analytic, and involve the charged hard sphere diameter as the only unknown parameter, which we determine using an approximate scaling property of the direct correlation function. Results obtained for structural correlation functions and various thermodynamic quantities are in very good agreement with the Monte Carlo simulation data.