Experimental results showing significant reductions from classical in the Rayleigh-Taylor instability growth rate due to high pressure effective lattice viscosity are presented. Using a laser created ramped drive, vanadium samples are compressed and accelerated quasi-isentropically at peak pressures, while maintaining the sample in the solid state. Comparisons with simulations and theory indicate that the high pressure, high strain rate conditions trigger a phonon drag mechanism, resulting in the observed high effective lattice viscosity and strong stabilization of the Rayleigh-Taylor instability.