Dynamic Monte Carlo simulations of the folding of a globular protein, apoplastocyanin, have been undertaken in the context of a new lattice model of proteins that includes both side chains and a-carbon backbone atoms and that can approximate native conformations at the level of 2 angstroms (root mean square) or better. Starting from random-coil unfolded states, the model apoplastocyanin was folded to a native conformation that is topologically similar to the real protein. The present simulations used a marginal propensity for local secondary structure consistent with but by no means enforcing the native conformation and a full hydrophobicity scale in which any nonbonded pair of side chains could interact. These molecules folded through a punctuated on-site mechanism of assembly where folding initiated at or near one of the turns ultimately found in the native conformation. Thus these simulations represent a partial solution to the globular-protein folding problem.