We report on the evolution of the thickness-dependent electronic band structure of the two-dimensional layered-dichalcogenide molybdenum disulfide (MoS2). Micrometer-scale angle-resolved photoemission spectroscopy of mechanically exfoliated and chemical-vapor-deposition-grown crystals provides direct evidence for the shifting of the valence band maximum from Γ to K, for the case of MoS2 having more than one layer, to the case of single-layer MoS2, as predicted by density functional theory. This evolution of the electronic structure from bulk to few-layer to monolayer MoS2 had earlier been predicted to arise from quantum confinement. Furthermore, one of the consequences of this progression in the electronic structure is the dramatic increase in the hole effective mass, in going from bulk to monolayer MoS2 at its Brillouin zone center, which is known as the cause for the decreased carrier mobility of the monolayer form compared to that of bulk MoS2.