  A recurring difficulty in the Minimal Model Program is that while log
terminal singularities are quite well behaved (for instance, they are
rational), log canonical singularities are much more complicated; they need not
even be Cohen-Macaulay. The aim of this paper is to prove that log canonical
singularities are Du Bois. The concept of Du Bois singularities, introduced by
Steenbrink, is a weakening of rationality. We also prove flatness of the
cohomology sheaves of the relative dualizing complex of a projective family
with Du Bois fibers. This implies that each connected component of the moduli
space of stable log varieties parametrizes either only Cohen-Macaulay or only
non-Cohen-Macaulay objects.
