How does a protein find its native state without a globally exhaustive search? We propose the "HZ" (hydrophobic zipper) hypothesis: hydrophobic contacts act as constraints that bring other contacts into spatial proximity, which then further constrain and zip up the next contacts, etc. In contrast to helix-coil cooperativity, HZ-heteropolymer collapse cooperativity is driven by nonlocal interactions, causes sheet and irregular conformations in addition to helices, leads to secondary structures concurrently with early hydrophobic core formation, is much more sequence dependent than helix-coil processes, and involves compact intermediate states that have much secondary--but little tertiary--structure. Hydrophobic contacts in the 1992 Protein Data Bank have the type of "topological localness" predicted by the hypothesis. The HZ paths for amino acid sequences that mimic crambin and bovine pancreatic trypsin inhibitor are quickly found by computer; the best configurations thus reached have single hydrophobic cores that are within about 3 kcal/mol of the global minimum. This hypothesis shows how proteins could find globally optimal states without exhaustive search.