We have developed a rapid and completely automatic method for prediction of protein side-chain conformation, applying the simulated annealing algorithm to optimization of side-chain packing (van der Waals) interactions. The method directly attacks the combinatorial problem of simultaneously predicting many residues' conformation, solving in 8 to 12 hours problems for which the systematic search would require over 10³⁰⁰ central processing unit years. Over a test set of nine proteins ranging in size from 46 to 323 residues, the program's predictions for side-chain atoms had a root-mean-square (r.m.s.) deviation of 1.77 Å overall versus the native structures. More importantly, the predictions for core residues were especially accurate, with an r.m.s. value of 1.25 Å overall: 80 to 90% of the large hydrophobic side-chains dominating the internal core were correctly predicted, versus 30 to 40% for most current methods. The predictions' main errors were in surface residues poorly constrained by packing and small residues with greater steric freedom and hydrogen bonding interactions, which were not included in the program's potential function. van der Waals interactions appear to be the supreme determinant of the arrangement of side-chains in the core, enforcing a unique allowed packing that in every case so far examined matches the native structure.