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In synthetic biological systems, rare events can cause undesirable behavior leading to pathological effects. Due to their low observability, rare events are challenging to analyze using existing stochastic simulation methods. Chemical Reaction Networks (CRNs) are a general-purpose formal language for modeling chemical kinetics. This paper presents a fully automated approach to efficiently construct a large number of concurrent traces by expanding a sample of known traces. These traces constitute a partial state space containing only traces leading to a rare event of interest. This state space is then used to compute a lower bound for the rare event’s probability. We propose a novel approach for the analysis of highly concurrent CRNs, including a CRN reaction independence analysis and an algorithm that exploits CRN concurrency to rapidly enumerate parallel traces. We then present a novel algorithm to add cycles to a partial state space to further increase the rare event’s probability lower bound to its actual value. The resulting prototype tool, RAGTIMER, demonstrates improvement over stochastic simulation and probabilistic model checking.