Cooper pairs with a finite center-of-mass momentum form a remarkable state in which the superconducting order parameter is modulated periodically in space. Although intense interest in such a “pair-density wave” (PDW) state has emerged due to recent discoveries in high T c superconductors, there is little theoretical understanding of the mechanism driving this exotic state. The challenge is that many competing states lie close in energy in seemingly simple models, such as the Hubbard model, in the strongly correlated regime. Here, we show that inversion symmetry breaking and the resulting spin-valley locking can promote PDWs over more commonly found spin stripes through frustration against magnetic order. Specifically, we find the first robust evidence for a PDW within density matrix renormalization group simulation of a simple fermionic model. Our results point to a tantalizing possibility in hole-doped group VI transition metal dichalcogenides, with spin-valley locked band structure and moderate correlations. Copyright © 2019 The Authors.