  We report epitaxial growth of vanadium diselenide (VSe$_2$) thin films in the
octahedrally-coordinated (1T) structure on GaAs(111)B substrates by molecular
beam epitaxy. Film thickness from a single monolayer (ML) up to 30 ML is
demonstrated. Structural and chemical studies using by x-ray diffraction,
transmission electron microscopy, scanning tunneling microscopy and x-ray
photoelectron spectroscopy indicate high quality thin films. Further studies
show that monolayer VSe$_2$ films on GaAs are not air-stable and are
susceptible to oxidation within a matter of hours, which indicates that a
protective capping layer should be employed for device applications. This work
demonstrates that VSe$_2$, a candidate van der Waals material for possible
spintronic and electronic applications, can be integrated with III-V
semiconductors via epitaxial growth for 2D/3D hybrid devices.
