The channeling enzyme tryptophan synthase provides a paradigmatic example of a chemical nanomachine. It possesses two active centers and, as a single molecule, catalyzes 13 different reaction steps with a complex pattern of allosteric regulation and with an intermediate product channeled from one active center to another. Here, the first single-molecule stochastic model of the enzyme is proposed and analyzed. All its transition rate constants were deduced from the experimental data available, and no, fitting parameters were thus employed. Numerical simulations reveal strong correlations in the states of the active centers and the emergent synchronization of intramolecular processes in tryptophan synthase.