  We discuss simple cosmological solutions of Horava-Witten theory describing
the strongly coupled heterotic string. At energies below the grand-unified
scale, the effective theory is five- not four-dimensional, where the additional
coordinate parameterizes a S^1/Z_2 orbifold. Furthermore, it admits no
homogeneous solutions. Rather, the vacuum state, appropriate for a reduction to
four-dimensional supersymmetric models, is a BPS domain wall. Relevant
cosmological solutions are those associated with this BPS state. In particular,
such solutions must be inhomogeneous, depending on the orbifold coordinate as
well as on time. We present two examples of this new type of cosmological
solution, obtained by separation of variables rather that by exchange of time
and radius coordinate applied to a brane solution, as in previous work. The
first example represents the analog of a rolling radii solution with the radii
specifying the geometry of the domain wall. This is generalized in the second
example to include a nontrivial ``Ramond-Ramond'' scalar.
