Cubic boron arsenide (c-BAs) is a promising ultrahigh thermal conductivity semiconductor, but its direct synthesis on lattice-mismatched substrates remains challenging. Here, we demonstrate the synthesis of nanocrystalline c-BAs thin films on GaAs(100) substrates using gas source molecular beam epitaxy. X-ray photoelectron spectroscopy reveals an optimal growth temperature window of 250-400 C to maintain near stoichiometry and suppress severe arsenic loss. Surface and structural characterizations via atomic force microscopy, reflection high-energy electron diffraction, and grazing-incidence X-ray diffraction demonstrate a Volmer-Weber 3D island growth mode and a preferential crystallographic alignment with the GaAs substrate. High-resolution transmission electron microscopy confirms a chemically sharp interface without gallium interdiffusion into the c-BAs layer. These findings establish an initial step for the integration of c-BAs into advanced thermal and optoelectronic platforms.