A "self-consistent field" theory based on the Bethe approximation and previously shown to reproduce the exact partition function for one-dimensional hard spheres at all densities and to give good results for classical harmonic and nearly harmonic crystals is applied to the three-dimensional hard-sphere system. Solutions of the resulting equations which are approximately valid at high densities are obtained. There are two possible solutions, one of which gives values for the entropy and one-particle distribution function in good agreement with results for the hard-sphere solid derived from computer simulations. The other solution may be associated with the fluid phase. Copyright © 1975 American Institute of Physics.