The high-pressure viscosities of four dilute, good-solvent polymer solutions [polystyrene (PS in tetrahydrofuran (THF) and chloroform, polyisobutylene (PIB) in THF, and partially hydrolyzed polyacrylamide (HPAM) in 2% NaCl-water] were measured in a new diamond-anvil cell viscometer at pressure up to 20 kbar. The viscosity of these polymer solutions rises faster with increasing pressure than the viscosity of the solvents in the absence of the polymers. The specific viscosity, eta(sp), was calculated at high pressure by obtaining the ratio of solution to solvent viscosity at each pressure. The intrinsic viscosity, [eta], was then calculated using the well-known Huggins equation. After the concentration is corrected to reflect decreasing solvent volume as a result of compression at high pressure, eta(sp) plotted against concentration falls on a single curve at all pressures. This curve is identical to the curve determined at ambient pressure. Thus [eta] is pressure invariant to within our experimental uncertainty, 10%. The application of simple dilute polymer solution theory further implies that the radius of gyration is also invariant with pressure. The implication of this finding is that the increase in eta(sp) with pressure arises solely from the increased volume fraction of the polymer per unit volume of the solvent.