The time evolution of a well-stirred chemically reacting system is traditionally modeled by a set of coupled ordinary differential equations called the reaction rate equation (RRE). The resulting picture of continuous deterministic evolution is, however, valid only for infinitely large systems. That condition is usually well approximated in laboratory test tube systems. But in biological systems formed by single living cells, the small population numbers of some reactant species can result in dynamical behavior that is noticeably discrete rather than continuous, and stochastic rather than deterministic. In that case, a more physically accurate mathematical modeling is obtained by using the machinery of Markov process theory, specifically, the chemical master equation (CME) and the stochastic simulation algorithm (SSA). After reviewing the theoretical foundations of stochastic chemical kinetics, we will describe a way to approximate the SSA by a faster simulation procedure, and then show how this way also provides a logical bridge between the CME/SSA description and the RRE description.