Molecular dynamics simulations have been used to compute the difference in the unfolding free energy between wild-type barnase and the mutant in which Ile-96 is replaced by alanine. The simulations yield results (-3.42 and -5.21 kcal/mol) that compare favorably with experimental values (-3.3 and -4.0 kcal/mol). The major contributions to the free energy difference arise from bonding terms involving degrees of freedom of the mutated side chain and from nonbonded interactions of that side chain with its environment in the folded protein. By comparison with simulations of an extended peptide in the absence of solvent, used as a reference state, hydration effects are shown to play a minor role in the overall free energy balance for the Ile----Ala transformation. The implications of these results for our understanding of the hydrophobic effect and its contribution to protein stability are discussed.