The kinetics of the binding reaction A + B reversible arrow C are solved exactly via the stochastic master equation, in which molecular populations are considered as time-dependent, integer-valued random variables. This transient solution extends previous work on the irreversible bimolecular reaction and the equilibrium state of the reversible bimolecular reaction. For small ensembles of reactants, comparisons are made between the results of the deterministic and stochastic approaches to the problem, and methods are presented to numerically evaluate the solution.