In this paper we present a new residue contact potential derived by statistical analysis of protein crystal structures. This gives mean hydrophobic and pairwise contact energies as a function of residue type and distance interval. To test the accuracy of this potential we generate model structures by "threading" different sequences through backbone folding motifs found in the structural data base. We find that conformational energies calculated by summing contact potentials show perfect specificity in matching the correct sequences with each globular folding motif in a 161-protein data set. They also identify correct models with the core folding motifs of hemerythrin and immunoglobulin McPC603 V1-domain, among millions of alternatives possible when we align subsequences with alpha-helices and beta-strands, and allow for variation in the lengths of intervening loops. We suggest that contact potentials reflect important constraints on nonbonded interaction in native proteins, and that "threading" may be useful for structure prediction by recognition of folding motif.