An efficient algorithm for the determination of an everywhere positive electron-density distribution that agrees with observed structure amplitudes has been used to determine the phases of X-ray diffraction data from recombinant bovine chymosin, a protein with 323 amino-acid residues in the molecular chain whose structure was recently determined using molecular replacement methods. A systematic procedure for testing the signs of centric reflections, using the total entropy of the map as a figure of merit, was used to produce a low-resolution map. The phases of acentric and additional centric reflections were then chosen by adding them to the map with various possible phases and computing the total entropy of the resulting map. Of 159 centric reflections whose phases were chosen by this procedure, 141 had the same phase as in the refined structure. The median absolute phase difference for 1811 acentric reflections was 32 degrees. A map produced from these 1970 reflections, out of 12,346 reflections in the data set, showed a remarkable agreement with the refined structure. This molecule is many times larger than any whose structures have previously been determined without the use of isomorphous replacement, molecular replacement or anomalous dispersion, and the map demonstrates the potential of maximum-entropy methods in macromolecular structure determination.