  We propose, within a perturbative string theory example, a cosmological way
to generate a large hierarchy between the observed Planck mass and the
fundamental string scale. Time evolution results in three large space
dimensions, one additional dimension transverse to our world and five small
internal dimensions with a very slow time evolution. The evolution of the
string coupling and internal space generate a large Planck mass. However due to
an exact compensation between the time evolution of the internal space and that
of the string coupling, the gauge and Yukawa couplings on our Universe are time
independent.
