Polarization transfer from hyperpolarized gas to H-1, C-13, etc. holds great promise for sensitivity enhancement of solution-state NMR. The route explored here uses hyperpolarized, supercritical xenon as solvent for the organic solute. A method is described for preparation of supercritical xenon solutions with little polarization loss. Detection of Overhauser enhancement of solute proton magnetization by factors of 3 to 7 confirms the intimate contact between Xe-129 and H-1. Motivated by more efficient polarization transfer expected in solid solutions, we report survival of non-equilibrium solute polarization upon warming from solid to supercritical fluid.