  A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a
description as an infra-red fixed point obtained by deforming the N=4
supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral
multiplets. We study the Penrose limit of the supergravity dual of the large n
limit of this N=1 gauge theory. The limit gives a pp-wave with R-R five-form
flux and both R-R and NS-NS three-form flux. We discover that this new solution
preserves twenty supercharges and that, in the light-cone gauge, string theory
on this background is exactly solvable. Correspondingly, this latter is the
stringy dual of a particular large charge limit of the large n gauge theory. We
are able to identify which operators in the field theory survive the limit to
form the string's ground state and some of the spacetime excitations. The full
string model, which we exhibit, contains a family of non-trivial predictions
for the properties of the gauge theory operators which survive the limit.
