Just as parallel threebranes on a smooth manifold are related to string the
ory on AdS(5) x S-5 parallel threebranes near a conical singularity are rel
ated to string theory on AdS(5) x X-5, for a suitable X-5. For the example
of the conifold singularity, for which X-5 = (SU(2) x SU(2))/U(1), we argue
that string theory on AdS(5) x X-5 can be described by a certain N = 1 sup
ersymmetric gauge theory which we describe in detail. (C) 1999 Elsevier Sci
ence B.V.