We present evidence of a BCS superfluid phase in the $3+1$ dimensionalNambu--Jona-Lasinio model at non-zero chemical potential $\mu$.Large-$N_c$ results are used to match the model's parameters tolow-energy, zero-density phenomenology.A lattice study of the fermionic sector yields thequasi-particle dispersion relation, which shows clearevidence of a BCS gap $\Delta\neq0$ in the high-$\mu$ phase.We also discuss the finite volume effects of a system with a Fermisurface.