  Recent understanding of {\cal N}=1* supersymmetric theory (mass deformed
{\cal N}=4) has made it possible to find an exact superpotential which encodes
the properties of the different phases of the theory. We consider this
superpotential as an illustrative example for the source of a nontrivial scalar
potential for the string theory dilaton and study its properties. The
superpotential is characterized by the rank of the corresponding gauge group
(N) and integers p,q,k labelling the different massive phases of the theory.
For generic values of these parameters, we find the expected runaway behaviour
of the potential to vanishing string coupling. But there are also
supersymmetric minima at weak coupling stabilizing the dilaton field. An
interesting property of this potential is that there is a proliferation of
supersymmetric vacua in the confining phases, with the number of vacua
increasing with N and leading to a kind of staircase potential. For a range of
parameters, it is possible to obtain realistic values for the gauge coupling.
