The paper introduces the τ-leap method, an approximate procedure for simulating chemically reacting systems that can significantly reduce simulation time while maintaining acceptable accuracy. The τ-leap method is based on the assumption that the propensity functions for reactions remain approximately constant over a small time interval, allowing for larger jumps in the system's state. The authors describe the τ-leap method, its connection to the chemical Langevin equation, and strategies for selecting appropriate parameters. They also present a refinement, the estimated-midpoint technique, which further reduces errors in the τ-leap method. Two simple model systems are used to demonstrate the effectiveness of the τ-leap method, showing that it can achieve substantial speed improvements with minimal loss of accuracy. The paper concludes with a discussion of the τ-leap method's potential for transitioning from exact stochastic simulation to deterministic reaction rate equations as system size increases.The paper introduces the τ-leap method, an approximate procedure for simulating chemically reacting systems that can significantly reduce simulation time while maintaining acceptable accuracy. The τ-leap method is based on the assumption that the propensity functions for reactions remain approximately constant over a small time interval, allowing for larger jumps in the system's state. The authors describe the τ-leap method, its connection to the chemical Langevin equation, and strategies for selecting appropriate parameters. They also present a refinement, the estimated-midpoint technique, which further reduces errors in the τ-leap method. Two simple model systems are used to demonstrate the effectiveness of the τ-leap method, showing that it can achieve substantial speed improvements with minimal loss of accuracy. The paper concludes with a discussion of the τ-leap method's potential for transitioning from exact stochastic simulation to deterministic reaction rate equations as system size increases.