The growth of high quality Si/GaAs superlattices on GaAs substrates using molecular beam epitaxy is described. A typical superlattice structure consisted of ten periods of thin (<5Å) layers of pseudomorphic silicon alternating with thick GaAs layers; typical GaAs thicknesses range from 100Å to 1850Å. In situ reflection high energy electron diffraction analysis of the structures during growth showed the silicon layers developed a (3 ×1) reconstruction, while the GaAs exhibited a (4×2)→(3×2)→(3×1)→(2×4) reconstruction sequence. Both observations agree with prior studies of the growth of embedded silicon in GaAs/Si/GaAs heterostructures. X-ray diffraction using the (004) reflection showed sharp and intense satellite peaks (out to 22 orders in one case), indicating a high level of structural quality. Very good agreement has been obtained between observed diffraction patterns and those calculated via dynamical simulation.