© 2017 American Chemical Society. Molecular beam epitaxy (MBE) provides a simple but powerful way to synthesize large-area high-quality thin films and heterostructures of a wide variety of materials including accomplished group III-V and II-VI semiconductors as well as newly developing oxides and chalcogenides, leading to major discoveries in condensed-matter physics. For two-dimensional (2D) materials, however, main fabrication routes have been mechanical exfoliation and chemical vapor deposition by making good use of weak van der Waals bonding nature between neighboring layers, and MBE growth of 2D materials, in particular on insulating substrates for transport measurements, has been limited despite its fundamental importance for future advanced research. Here, we report layer-by-layer epitaxial growth of scalable transition-metal dichalocogenide (TMDC) thin films on insulating substrates by MBE and demonstrate ambipolar transistor operation. The proposed growth protocol is broadly applicable to other TMDCs, providing a key milestone toward fabrication of van der Waals heterostructures with various 2D materials for novel properties and functionalities.