The detailed behavior of many molecular processes in the cell, such as protein folding, protein complex assembly, and gene regulation, transcription and translation, can often be accurately captured by stochastic chemical kinetic models. We investigate a novel computational problem involving these models---that of finding the most probable sequence of reactions that connects two or more states of the system observed at different times. We describe an efficient method for computing the probability of a given reaction sequence, but argue that computing most probable reaction sequences is EXPSPACE-hard. We develop exact (exhaustive) and approximate algorithms for finding most probable reaction sequences. We evaluate these methods on test problems relating to a recently-proposed stochastic model of folding of the Trp-cage peptide. Our results provide new computational tools for analyzing stochastic chemical models, and demonstrate their utility in illuminating the behavior of real-world systems.