We have predicted that difluoromethane (CH2F2) will be the highest-affinity guest for Rebek's "tennis ball" host(1) using a new approach to multimolecule free energy calculations. The method, which we call chemical-Monte Carlo/Molecular Dynamics (CMC/MD), was first tested by calculating the relative free energies of solvation of a variety of molecules. Subsequently, we have used it to compare nine possible guests binding to the "tennis ball" host and predict that CH2F2 will bind more tightly to this host than CH4, the strongest binding guest studied to date. This prediction has been supported by standard thermodynamic integration free energy calculations in which CH4 was mutated into CH2F2 both in solution and in the host. Our results show the full power of such multimolecule calculations-namely, that they can be used to rapidly calculate and rank the relative binding free energies of many molecules from a single simulation,. accelerating the discovery of novel ligands or guests.