We point out that SO(2Nc) gauge theory with Nf fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential μB. One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2Nc) theory is particularly interesting because a wide class of observables in the SO(2Nc) theory coincide with observables in QCD in the large Nc limit, as we show using the technique of large Nc orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at finite μB provided one adds appropriate deformation terms to the SO(2Nc) theory. This opens up the prospect of learning about QCD at finite μB using lattice studies of the SO(2Nc) theory.