We are conducting an experiment to search for WIMPs, or weakly-interacting massive particles, in the galactic halo using terrestrial detectors. This generic class of hypothetical particles, whose properties are similar to those predicted by extensions of the standard model of particle physics, could comprise the cold component of non-baryonic dark matter. We describe our experiment, which is based on cooled germanium and silicon detectors in a shielded low-background cryostat. The detectors achieve a high degree of background rejection through the simultaneous measurement of the energy in phonons and ionization. Using exposures on the order of one kilogram-day from initial runs of our experiment, we have achieved (preliminary) upper limits on the WIMP-nucleon cross section that are comparable to much longer runs of other experiments.