We have measured the isotropic Raman CH stretching spectrum of cyclohexane-d(11) in supercritical CO2 at 49.7 degrees C and in liquid CO2 at room temperature over a range of densities from 0.2 rho(c) to 2 rho(c), where the critical number density rho(c) for CO2 is 6.4 nm(-3). The axial and equatorial CH stretching bands in the spectrum shift to lower frequencies and broaden with increasing density. As was the case in an earlier study of cyclohexane-d(11) in liquid solvents [G. J. Remar and R. A. MacPhail, J. Chem. Phys. 103, 4381 (1995)], the "perturbed hard-fluid model" of Ben-Amotz and Herschbach provides a satisfyingly consistent description of the observed shifts in terms of competing contributions from repulsive and attractive solute-solvent forces along the CH bond. In particular, when the repulsive contribution to the shift is calculated according to the prescription developed in the liquid solution study, the attractive contribution is found to scale linearly with the density and with the polarizability derivative of the CH bond, as predicted by the model. The ratio of the equatorial to axial linewidths has a density-independent value of 1.2, nearly the same value found for the liquid solutions and numerically equivalent to the ratio of polarizability derivatives for the CH bonds. This equivalence is consistent with Schweizer and Chandler＇s theoretical result for the width of a band that is inhomogeneously broadened by attractive force fluctuations, but the density dependence is not; their result would predict a nonlinear density dependence with a maximum near rho(c), whereas the observed linewidths show a nearly linear dependence on density. Neither the frequency shifts nor the linewidths show any clear evidence for a "local solvent density enhancement" that would be predicted for this mixture near the critical point. In the accompanying paper, Frankland and Maroncelli describe molecular-dynamics simulations of cyclohexane in supercritical CO2 that reproduce the observed linewidths nearly quantitatively. They show convincing evidence that the linewidths are dominated by binary, collisional interactions between the hydrogen and the solvent, and they discuss the apparent absence of a density enhancement.