Tunable bandgaps(1), extraordinarily large exciton-binding energies(2,3), strong light-matter coupling(4) and a locking of the electron spin with layer and valley pseudospins(5-8) have established transition-metal dichalcogenides (TMDs) as a unique class of two-dimensional (2D) semiconductors with wide-ranging practical applications(9,10). Using angle-resolved photoemission (ARPES), we show here that doping electrons at the surface of the prototypical strong spin-orbit TMD WSe2, akin to applying a gate voltage in a transistor-type device, induces a counterintuitive lowering of the surface chemical potential concomitant with the formation of a multivalley 2D electron gas (2DEG). These measurements provide a direct spectroscopic signature of negative electronic compressibility (NEC), a result of electron-electron interactions, which we find persists to carrier densities approximately three orders of magnitude higher than in typical semiconductor 2DEGs that exhibit this effect(11,12). An accompanying tunable spin splitting of the valence bands further reveals a complex interplay between single-particle band-structure evolution and many-body interactions in electrostatically doped TMDs. Understanding and exploiting this will open up new opportunities for advanced electronic and quantum-logic devices.