A magnetically levitated sphere rheometer (MLSR) designed to measure viscosity of fluids exposed to high-pressure carbon dioxide has been developed. This device consists of a magnetic sphere submerged inside a test fluid within a high-pressure housing and levitated at a fixed point. The housing is constructed from an optically transparent sapphire tube. The cylindrical tube can be moved vertically to generate a shear flow around the levitated sphere. The difference in magnetic force required to levitate the sphere at rest and under fluid motion can be directly related to fluid viscosity. Rheological properties, specifically zero shear viscosities, of transparent high-pressure materials can be measured to a precision of about 5% and over a wide range of viscosities. In addition, operation at constant pressure, in concentration regimes from a pure polymer to an equilibrated polymer/supercritical fluid solution, and at shear rates over several orders of magnitude is possible, eliminating many of the disadvantages associated with other high-pressure rheometers. Experiments performed at different temperatures with a poly(dimethylsiloxane) melt at atmospheric pressure are compared with data from a commercial Couette rheometer to demonstrate device sensitivity and viability. Measurements of a PDMS melt plasticized by high-pressure CO2 are performed to illustrate the utility of the new rheometer under high-pressure conditions. Experimental data are obtained at 30 degreesC, for pressures up to 20.7 MPa and CO2 concentrations reaching 30 wt%. Viscosity reductions of nearly two orders of magnitude compared with the pure polymer viscosity at atmospheric pressure are-observed. Additionally, the effects of pressure on a polymer/CO2 system are directly investigated taking advantage of the constant pressure operation mode of the MLSR. This allows us, for the first time in experiments of polymers with supercritical fluids, to decouple the effects Of CO2 concentration and pressure in a single device.