Heteroepitaxial thin films of Si have been deposited onto GaP and GaAs substrates at low temperatures, <400-degrees-C, by remote plasma-enhanced chemical vapor deposition. Cleaning and passivation of the GaP and GaAs surfaces, by ex situ wet chemistry, and in situ exposure to atomic-H at temperatures from 400 to 530-degrees-C, were found to be critical in promoting epitaxial growth. The exposure to atomic-H was effective in removing surface oxides and hydrocarbon contamination. After the H-exposure, low energy electron diffraction (LEED) measurements revealed an ordered 1 X 1 structure for the GaP(111) surface, and a c(8 X 2)Ga structure for the GaAs(100) surface. Heteroepitaxial films of Si have been deposited at temperatures from 300 to 400-degrees-C and pressures between 50 and 500 mTorr, with the highest quality epitaxial growth proceeding on vicinal GaP(100) surfaces. In contrast, for the growth of Si on GaP(111) and GaAs(100) surfaces, LEED measurements indicate the onset of strain-induced disorder within the first few monolayers of the Si overgrowth.