At the cellular scale, biochemical processes are governed by random interactions between reactant molecules with small copy counts, leading to behavior that is inherently stochastic. Such systems are often modeled as continuous-time Markov jump processes that can be described by the Chemical Master Equation. Gillespie's Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems. The amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly as the problem size increases. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity. Optimal algorithm parameters and binning strategies are discussed. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large models that can be described by the Reaction-Diffusion Master Equation arising from spatially discretized reaction-diffusion processes.