The thermodynamic properties of hydrogen gas in liquid water are investigated using Monte Carlo molecular simulation and the quasichemical theory of liquids. The free energy of hydrogen hydration obtained by Monte Carlo simulations agrees well with the experimental result, indicating that the classical force fields used in this work provide an adequate description of intermolecular interactions in the aqueous hydrogen system. Two estimates of the hydration free energy for hydrogen made within the framework of the quasichemical theory also agree reasonably well with experiment provided local anharmonic motions and distant interactions with explicit solvent are treated. Both quasichemical estimates indicate that the hydration free energy results from a balance between chemical association and molecular packing. Additionally, the results suggest that the molecular packing term is almost equally driven by unfavorable enthalpic and entropic components.