An adaptation of the particle-particle/particle-mesh (P(3)M) code to the special purpose hardware GRAPE is presented. The short-range force is calculated by a four-chip GRAPE-3A board, while the rest of the calculation is performed on a Sun SPARC 10/51 workstation. The limited precision of the GRAPE hardware and algorithm constraints introduce stochastic errors of the order of a few percent in the gravitational forces. Tests of this new P3MG3A code show that it is a robust tool for cosmological simulations. The code currently achieves a peak efficiency of one-third the speed of the vectorized P(3)M code on a Gray C-90, and significant improvements are planned in the near future. Special purpose computers like GRAPE are therefore an attractive alternative to supercomputers for numerical cosmology.