Gödel universes in string theory

We show that homogeneous Gödel spacetimes need not contain closed timelike curves in low-energy-effective string theories. We find exact solutions for the Gödel metric in string theory for the full O(α^′) action including both dilaton and axion fields. The results are valid for bosonic, heterotic and super-strings. To first order in the inverse string tension α^′, these solutions display a simple relation between the angular velocity of the Gödel universe, Ω, and the inverse string tension of the form α^′=1/Ω² in the absence of the axion field. The generalization of this relationship is also found when the axion field is present.