  We investigate barotropic perfect fluid cosmologies which admit an isotropic
singularity. From the General Vorticity Result of Scott, it is known that these
cosmologies must be irrotational. In this paper we prove, using two different
methods, that if we make the additional assumption that the perfect fluid is
shear-free, then the fluid flow must be geodesic. This then implies that the
only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic
singularity are the FRW models.
