We have calculated total and binding energies of zinc-blende-structure boron nitride. Starting from a self-consistent-field ground-state calculation within a finite basis of Gaussian orbitals centered at the different atoms, the electron correlations were treated by applying the local ansatz. The electronic correlations are predominantly short ranged, as was also found for its isostructural compound, diamond. Of specific importance are correlations on the atomic scale. Electrons correlate strongly at the nitrogen atoms. The correlation strength within the B-N bonds and the reduction of the total-atomic-charge fluctuations is discussed in detail. For an agreement between calculated and experimental binding energies, additional basis functions on interstitial sites turned out to be necessary. Without them, correlations in the interstitial regions are too poorly covered. Such an effect should be relevant for all future calculations on open-structure materials. The final results for the binding energy compare well with calculations made within the local-density approximation.