A method of stochastic simulation is applied to the Brusselator chemical reactions and used to model the time course of chemical abundances in this system. Statistical ensembles are used to calculate the nonequilibrium probability density and the expectation values of the reactant concentrations. The time development of the expectation values is found to depend in a novel manner on the thermodynamic size of the system. The first moments of the ensemble do not remain on or near the limit cycle; in contrast to the solutions of the deterministic reaction-rate equations they spiral inward toward the center of the limit cycle in a manner determined by the thermodynamic size of the system. Previously predicted, this behavior has not heretofore been observed in an actual system or computational model. The evolution is found to exhibit multiple time scales in which there is a fast initial decay proportional to the overall time required for phase decorrelation. Mechanisms for this scaling are discussed. The general structure of the evolving ensemble is found to be related to the ‘‘weak retrace property’’ of the Brusselator, in which portions of the periodic trajectory are unable to follow the path laid down on earlier oscillations. The weak retrace phenomenon is studied for members of the statistical ensemble and a general mechanism for it proposed.