  Killing forms on Riemannian manifolds are differential forms whose covariant
derivative is totally skew--symmetric. We show that a compact simply connected
symmetric space carries a non--parallel Killing $p$--form ($p\ge2$) if and only
if it isometric to a Riemannian product $S^k\times N$, where $S^k$ is a round
sphere and $k>p$.
