  The metallic transition-metal dichalcogenides (TMDCs) are benchmark systems
for studying and controlling intertwined electronic orders in solids, with
superconductivity developing upon cooling from a charge density wave state. The
interplay between such phases is thought to play a critical role in the
unconventional superconductivity of cuprates, Fe-based, and heavy-fermion
systems, yet even for the more moderately-correlated TMDCs, their nature and
origins have proved highly controversial. Here, we study a prototypical
example, $2H$-NbSe$_2$, by spin- and angle-resolved photoemission and
first-principles theory. We find that the normal state, from which its hallmark
collective phases emerge, is characterised by quasiparticles whose spin is
locked to their valley pseudospin. This results from a combination of strong
spin-orbit interactions and local inversion symmetry breaking. Non-negligible
interlayer coupling further drives a rich three-dimensional momentum-dependence
of the underlying Fermi surface spin texture. Together, these findings
necessitate a fundamental re-investigation of the nature of charge order and
superconducting pairing in NbSe$_2$ and related TMDCs.
