Expansion of supersymmetric string theory suggests that the leading quadratic curvature correction to the Einstein action is the Gauss-Bonnet invariant. We show that this model has both flat and anti-de Sitter space as solutions, but that the cosmological branch is unstable, because the graviton becomes a ghost there: The theory solves its own cosmological problem. The general static spherically symmetric solution is exhibited; it is asymptotically Schwarzschild. The sign of the Gauss-Bonnet coefficient determines whether there is a normal event horizon (for the string-generated sign) or a naked singularity. We discuss the effects of higher-curvature corrections and of an explicit cosmological term on stability.