  Most models of inflation have small parameters, either to guarantee
sufficient inflation or the correct magnitude of the density perturbations. In
this paper we show that, in supersymmetric theories with weak scale
supersymmetry breaking, one can construct viable inflationary models in which
the requisite parameters appear naturally in the form of the ratio of mass
scales that are already present in the theory. Successful inflationary models
can be constructed from the flat-direction fields of a renormalizable
supersymmetric potential, and such models can be realized even in the context
of a simple GUT extension of the MSSM. We evade naive ``naturalness" arguments
by allowing for more than one field to be relevant to inflation, as in ``hybrid
inflation" models, and we argue that this is the most natural possibility if
inflaton fields are to be associated with flat direction fields of a
supersymmetric theory. Such models predict a very low Hubble constant during
inflation, of order $10^3$-$10^4$ GeV, a scalar density perturbation index $n$
which is very close to or greater than unity, and negligible tensor
perturbations. In addition, these models lead to a large spike in the density
perturbation spectrum at short wavelengths.
