Realization of unconventional physical properties in two-dimensional (2D) transition-metal dichalcogenides (TMDs) is currently one of the key challenges in condensed-matter systems. However, the electronic properties of 2D TMDs remain largely unexplored compared to those of their bulk counterparts. Here, we report the fabrication of a high-quality monolayer NbSe 2 film with a trigonal prismatic structure by molecular beam epitaxy, and the study of its electronic properties by scanning tunneling microscopy, angleresolved photoemission spectroscopy, and electrical transport measurements, together with first-principles band-structure calculations. In addition to a charge density wave (CDW) with 3 × 3 periodicity and superconductivity below 1.5 K, we observed sizable (~0.1 eV) band splitting along the Γ-K cut in the Brillouin zone due to inversion symmetry breaking in the monolayer crystal. This splitting is highly anisotropic in k space, leading to a spin-split van-Hove singularity in the band structure. The present results suggest the importance of spin-orbit coupling and symmetry breaking for unconventional superconductivity and CDW properties in monolayer TMDs.