  We construct a model of non-uniform condensate having a spatially modulated
complex order parameter that makes it kinematically an x-ray solid, i.e., a
real mass density wave, but one admitting an associated superfluid flow.
Intrinsic to this state is a non-classical translational inertia which we
derive for the case of a potential flow. Connection to the non-classical
rotational inertia observed in recent experiments on solid helium-4 is
discussed. Our semi-phenomenological treatment suggests a flow-induced
supersolid-to-superdfluid transition.
