We present an approach to reconstructing chemical reaction networks from time series measurements of the concentrations of the molecules involved. Our solution strategy combines techniques from numerical sensitivity analysis and probabilistic graphical models. By modeling a chemical reaction system as a Markov network (undirected graphical model), we show how systematically probing for sensitivities between molecular species can identify the topology of the network. Given the topology, our approach next uses detailed sensitivity profiles to characterize properties of reactions such as reversibility, enzyme-catalysis, and the precise stoichiometries of the reactants and products. We demonstrate applications to reconstructing key biological systems including the yeast cell cycle. In addition to network reconstruction, our algorithm finds applications in model reduction and model comprehension. We argue that our reconstruction algorithm can serve as an important primitive for data mining...