  We report calculations of the electronic structure of CaB$_6$ using the
weighted density approximation (WDA) to density functional theory. We find a
semiconducting band structure with a sizable gap, in contrast to local density
approximation (LDA) results, but in accord with recent experimental data. In
particular, we find an $X$-point band gap of 0.8 eV. The WDA correction of the
LDA error in describing the electronic structure of CaB$_6$ is discussed in
terms of the orbital character of the bands and the better cancelation of
self-interactions within the WDA.
