  A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical
sheaf is a line bundle. This property, which measures the ``pathology'' of the
singularities of a variety, is thus stronger than Cohen-Macualayness, but is
also weaker than smoothness. We determine which Schubert varieties are
Gorenstein in terms of a combinatorial characterization using generalized
pattern avoidance conditions. We also give an explicit description as a line
bundle of the canonical sheaf of a Gorenstein Schubert variety.
