  We consider the effects of a gas of closed strings (treated quantum
mechanically) on a background where one dimension is compactified on a circle.
After we address the effects of a time dependent background on aspects of the
string spectrum that concern us, we derive the energy-momentum tensor for a
string gas and investigate the resulting space-time dynamics. We show that a
variety of trajectories are possible for the radius of the compactified
dimension, depending on the nature of the string gas, including a demonstration
within the context of General Relativity (i.e. without a dilaton) of a solution
where the radius of the extra dimension oscillates about the self-dual radius,
without invoking matter that violates the various energy conditions. In
particular, we find that in the case where the string gas is in thermal
equilibrium, the radius of the compactified dimension dynamically stabilizes at
the self-dual radius, after which a period of usual Friedmann-Robertson-Walker
cosmology of the three uncompactified dimensions can set in. We show that our
radion stabilization mechanism requires a stringy realization of inflation as
scalar field driven inflation invalidates our mechanism. We also show that our
stabilization mechanism is consistent with observational bounds.
