The results of linear augmented-plane-wave band calculations for cubic FeSi, carried out in the local-density approximation, predict a small (-0.11 eV) indirect semiconductor gap which agrees well with empirical estimates (-0.13 eV). The origin of this gap, which occurs within the Fe (3d) manifold, can be traced to a pseudogap that is present in the reference rocksalt phase that underlies the lower-symmetry FeSi structure. The relationship between the FeSi band structure and several types of many-body correlation mechanisms that have been advanced to explain its anomalous temperature-dependent magnetic properties is discussed