  Thin films of superfluid $^3$He were predicted, based on weak-coupling BCS
theory, to have a stable phase which spontaneously breaks translational
symmetry in the plane of the film. This crystalline superfluid, or "stripe"
phase, develops as a one dimensional periodic array of domain walls separating
degenerate B phase domains. We report calculations of the phases and phase
diagram for superfluid $^3$He in thin films using a strong-coupling
Ginzburg-Landau theory that accurately reproduces the bulk $^3$He superfluid
phase diagram. We find that the stability of the Stripe phase is diminished
relative to the A phase, but the Stripe phase is stable in a large range of
temperatures, pressures, confinement, and surface conditions.
