Transition metal dichalcogenides (TMDCs), together with other two-dimensional (2D) materials, have attracted great interest due to the unique optical and electrical properties of atomically thin layers. In order to fulfill their potential, developing large-area growth and understanding the properties of TMDCs have become crucial. Here, we have used molecular beam epitaxy (MBE) to grow atomically thin MoSe2 on GaAs(111)B. No intermediate compounds were detected at the interface of as-grown films. Careful optimization of the growth temperature can result in the growth of highly aligned films with only two possible crystalline orientations due to broken inversion symmetry. As-grown films can be transferred onto insulating substrates, allowing their optical and electrical properties to be probed. By using polymer electrolyte gating, we have achieved ambipolar transport in MBE-grown MoSe2. The temperature-dependent transport characteristics can be explained by the 2D variable-range hopping (2D-VRH) model, indicating that the transport is strongly limited by the disorder in the film.