The existence of a global in time strong solution for Cahn-Hilliard-Hele-Shaw equation, is explored. Such an equation can be viewed as a specialized conserved gradient flow with respect to the standard Cahn-Hilliard energy. The velocity vector is determined by the phase variable by either the Darcy law or a static Stokes equation. If the Darcy law is imposed, a local in time strong solution has been established in earlier literature. Instead, if a static Stokes equation is formulated to update the velocity, we present a global in time strong solution in this talk.