  We show that homogeneous G\"odel spacetimes need not contain closed timelike
curves in low-energy-effective string theories. We find exact solutions for the
G\"odel metric in string theory for the full $O(\alpha ^{\prime})$ 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
$\alpha ^{\prime}$, these solutions display a simple relation between the
angular velocity of the G\"odel universe, $\Omega ,$ and the inverse string
tension of the form $\alpha ^{\prime}=1/\Omega ^2$ in the absence of the axion
field. The generalization of this relationship is also found when the axion
field is present.
