  We argue that the heterotic string does not have classical vacua
corresponding to de Sitter space-times of dimension four or higher. The same
conclusion applies to type II vacua in the absence of RR fluxes. Our argument
extends prior supergravity no-go results to regimes of high curvature. We
discuss the interpretation of the heterotic result from the perspective of dual
type II orientifold constructions. Our result suggests that the genericity
arguments used in string landscape discussions should be viewed with caution.
