  It has been argued that rather generic features of string-inspired
inflationary theories with low-energy supersymmetry (SUSY) make it difficult to
achieve inflation with a Hubble scale H > m_{3/2}, where m_{3/2} is the
gravitino mass in the SUSY-breaking vacuum state. We present a class of
string-inspired supergravity realizations of chaotic inflation where a simple,
dynamical mechanism yields hierarchically small scales of post-inflationary
supersymmetry breaking. Within these toy models we can easily achieve small
ratios between m_{3/2} and the Hubble scale of inflation. This is possible
because the expectation value of the superpotential <W> relaxes from large to
small values during the course of inflation. However, our toy models do not
provide a reasonable fit to cosmological data if one sets the SUSY-breaking
scale to m_{3/2} < TeV. Our work is a small step towards relieving the apparent
tension between high-scale inflation and low-scale supersymmetry breaking in
string compactifications.
