We present experimental evidence of enhancement of the Forster energy transfer interaction in bilayer, optical microcavities incorporating CdSe nanocrystals and an organic dye. On optical excitation of the nanocrystal layer, we observe luminescence predominantly at wavelengths associated with emission from the dye, indicating that energy transfer is taking place. No significant energy transfer is observed in the absence of the microcavity, nor in a microcavity where the dye and nanocrystal layers are separated by a 20 nm spacer layer. We estimate that the Forster transfer rate is increased by at least a factor of 10 in the microcavity.