When designing and analyzing genetic circuits, researchers are often interested in the probability of the system reaching a given state within a certain amount of time. Usually, this involves simulating the system to produce some time series data and analyzing this data to discern the state probabilities. However, as the complexity of models of genetic circuits grow, it becomes more difficult for researchers to reason about the different states by looking only at time series simulation results of the models. To address this problem, this paper employs the use of stochastic model checking, a method for determining the likelihood that certain events occur in a system, with continuous stochastic logic (CSL) properties to obtain similar results. This goal is accomplished by the introduction of a methodology for converting a genetic circuit model (GCM) into a continuous-time Markov chain (CTMC). This CTMC is analyzed using transient Markov chain analysis to determine the likelihood that the circuit satisfies a given CSL property in a finite amount of time. This paper illustrates a use of this methodology to determine the likelihood of failure in a genetic toggle switch and compares these results to stochastic simulation-based analysis of this same circuit. Our results show that this method results in a substantial speedup as compared with conventional simulation-based approaches.