Heterogeneous engineering of two-dimensional layered materials, including metallic graphene and semiconducting transition metal dichalcogenides, presents an exciting opportunity to produce highly tunable electronic and optoelectronic systems. We report the direct growth of highly crystalline, monolayer tungsten diselenide (WSe2) on epitaxial graphene (EG). Raman spectroscopy and photoluminescence confirms high-quality WSe2 monolayers; while transmission electron microscopy shows an atomically sharp interface and low energy electron diffraction confirms near perfect orientation between WSe2 and EG. Vertical transport measurements across the WSe2/EG heterostructure provides evidence that a tunnel barrier exists due to the van der Waals gap, and is supported by density functional theory that predicts a 1.6 eV barrier for transport from WSe2 to graphene.