  Two-dimensional transition metal dichalcogenides with strong spin-orbit
interactions and valley-dependent Berry curvature effects have attracted
tremendous recent interests. Although novel single-particle and excitonic
phenomena related to spin-valley coupling have been extensively studied,
effects of spin-momentum locking on collective quantum phenomena remain
unexplored. Here we report an observation of superconducting monolayer NbSe$_2$
with an in-plane upper critical field over six times of the Pauli paramagnetic
limit by magneto-transport measurements. The effect can be understood in terms
of the competing Zeeman effect and large intrinsic spin-orbit interactions in
non-centrosymmetric NbSe$_2$ monolayers, where the electronic spin is locked to
the out-of-plane direction. Our results provide a strong evidence of
unconventional Ising pairing protected by spin-momentum locking and open up a
new avenue for studies of non-centrosymmetric superconductivity with unique
spin and valley degrees of freedom in the exact two-dimensional limit.
