Determining how a protein folds is a central problem in structural biology. The rate of folding of many proteins is determined by the transition state, so that a knowledge of its structure is essential for understanding the protein folding reaction. Here we use mutation measurements--which determine the role of individual residues in stabilizing the transition state--as restraints in a Monte Carlo sampling procedure to determine the ensemble of structures that make up the transition state. We apply this approach to the experimental data for the 98-residue protein acylphosphatase, and obtain a transition-state ensemble with the native-state topology and an average root-mean-square deviation of 6 A from the native structure. Although about 20 residues with small positional fluctuations form the structural core of this transition state, the native-like contact network of only three of these residues is sufficient to determine the overall fold of the protein. This result reveals how a nucleation mechanism involving a small number of key residues can lead to folding of a polypeptide chain to its unique native-state structure.