Electrons in monolayer transition metal dichalcogenides are characterized by valley and spin quantum degrees of freedom, making it possible to explore new physical phenomena and to foresee novel applications in the fields of electronics and optoelectronics. Theoretical proposals further suggest that Berry curvature effects, together with strong spin-orbit interactions, can generate unconventional Landau levels (LLs) under a perpendicular magnetic field. In particular, these would support valley- and spin-polarized chiral edge states in the quantum Hall regime. However, this unique LL structure has not been observed experimentally in transition metal dichalcogenides. Here we report the observation of fully valley- and spin-polarized LLs in high-quality WSe2 monolayers achieved by exploiting a van der Waals heterostructure device platform. We applied handedness-resolved optical reflection spectroscopy to probe the inter-LL transitions at individual valleys and derived the LL structure in turn. We also measured a sizeable doping-induced mass renormalization driven by the strong Coulomb interactions.