The presentation of potentially pathogenic peptides by major histocompatibility complex (MHC) molecules is one of the most important processes in adaptive immune defense. Prediction of peptide–MHC (pMHC) binding affinities is therefore a principal objective of theoretical immunology. Machine learning techniques achieve good results if substantial experimental training data are available. Approaches based on structural information become necessary if sufficiently similar training data are unavailable for a specific MHC allele, although they have often been deemed to lack accuracy. In this study, we use a free energy method to rank the binding affinities of 12 diverse peptides bound by a class I MHC molecule HLA-A*02:01. The method is based on enhanced sampling of molecular dynamics calculations in combination with a continuum solvent approximation and includes estimates of the configurational entropy based on either a one or a three trajectory protocol. It produces precise and reproducible free energy estimates which correlate well with experimental measurements. If the results are combined with an amino acid hydrophobicity scale, then an extremely good ranking of peptide binding affinities emerges. Our approach is rapid, robust, and applicable to a wide range of ligand–receptor interactions without further adjustment.