We carry out expanded ensemble Monte Carlo simulations in order to calculate the chemical potentials of carbon dioxide as solvent and those of hydrocarbons as solutes at supercritical conditions. Recently developed adaptive method is employed to find weight factors during the simulation, which is crucial to achieving high accuracy for free energy calculation. The present simulation method enables us to obtain chemical potentials of large solute molecules dissolved in compressed phase from a single run of simulation. Simulation results for the excess chemical potentials of pure carbon dioxide at 300, 325 and 350 K are compared with experimental data and values predicted by the Peng-Robinson equation of state. A good agreement is found for high pressures up to 500 bar. The chemical potentials of hydrocarbon solutes dissolved in carbon dioxide at infinite dilution are predicted by simulation. Less than eight intermediate subensembles are required to gradually insert (or delete) hydrocarbon solute molecules from methane to noctane into dense CO2 phase of approximately 1.0 g cm^(-3).