This data demonstrates the rotationally commensurate growth of atomically thin MoS2 on epitaxial graphene (EG) on silicon carbide using chemical vapor deposition. The characterization of the MoS2/EG heterostructure is performed using atomic force microscopy, Raman spectroscopy, X-ray photoelectron spectroscopy, synchrotron X-ray scattering, atomic-resolution scanning tunneling microscopy (STM), and scanning tunneling spectroscopy. DOI: 10.1021/acsnano.5b06398