  We present a class of exact solutions for homogeneous, anisotropic
cosmologies in four dimensions derived from the low-energy string effective
action including a homogeneous dilaton $\phi$ and antisymmetric tensor
potential $B_{\mu\nu}$. Making this potential time-dependent produces an
anisotropic energy-momentum tensor, and leads us to consider a Bianchi I
cosmology. The solution for the axion field must then only be a linear function
of one spatial coordinate. This in turn places an upper bound on the product of
the two scale factors evolving perpendicular to the gradient of the axion
field. The only late-time isotropic solution is then a {\em contracting}
universe.
