Nucleic acid-based technologies such as oligonucleotide microarrays typically feature thousands of chemical species, often designed to interact with only one other species such as cDNA, cRNA, or another nucleic acid polymer. Inasmuch as there are only four nucleotides employed in any given technological platform, and both probe and target species are serquences thereof, all DNA species may hybridize with each other, albeit weakly. Therefore, the design of oligonucleotide probes for microarrays that will preferentially hybridize to only one cDNA molecule must account for the possibility of thousands of confounding variables. Quantification of the population dynamics of such highly interconnected reaction networks, however, presents considerable computational obstacles. In this paper we present an exact method of characterizing the stochastic time evolution and equilibria of such highly-coupled reaction networks. Using this technique, we have simulated the hybridization of the entire S cerevisiae transcriptome to a genome of probes for the first time. Such types of simulations were heretofore impossible without the use of supercomputers, but may be performed on PCs within hours using our algorithm. Moreover, they may be used to characterize the robustness of a wide variety of genomic technologies including microarray designs, small-interfering RNA (siRNA) fidelity for RNA interference (RNAi), and massively parallel sequencing (MPSS).