Along with the growth of technologies allowing accurate visualization of biochemical reactions to the scale of individual molecules has arisen an appreciation of the role of statistical fluctuations in intracellular biochemistry. The stochastic nature of metabolism can no longer be ignored. It can be probed empirically, and theoretical studies have established its importance. Traditional methods for modeling stochastic biochemistry are derived from an elegant and physically satisfying theory developed by Gillespie. However, although Gillespie's algorithm and its derivatives efficiently model small-scale systems, complex networks are harder to manage on easily available computer systems. Here we present a novel method of simulating stochastic biochemical networks using discrete events simulation techniques borrowed from manufacturing production systems. The method is very general and can be mapped to an arbitrarily complex network. As an illustration, we apply the technique to the glucose phosphorylation steps of the Embden-Meyerhof-Parnas pathway in E. coli. We show that a deterministic version of the discrete event simulation reproduces the behavior of an analogous deterministic differential equation model. The stochastic version of the same model predicts that catastrophic bottlenecks in the system are more likely than one would expect from deterministic theory.