The petroleum system concept spans the spatial and temporal extent of all elements and processes required for the generation and preservation of petroleum. The critical moment of a petroleum system is the moment with the highest probability for the generation-migration-accumulation of hydrocarbons. It is an important concept in petroleum exploration risk assessment because the stratigraphic and geographic extents of a petroleum system are determined at the critical moment. In petroleum systems, thermal history data, burial history data, and vitrinite reflectance data may be unavailable, unreliable, or incomplete; this introduces significant uncertainty in the choice of the critical moment. We present here a quantitative probabilistic framework for estimating the critical moment and quantifying the associated uncertainty in such cases. We define a probabilistic early bound and late bound for the critical moment (which, combined together, we term the critical range) and then estimate the moment with the highest numerical probability of generation-migration-accumulation. We define the uncertainty associated with the critical moment as half the absolute value of the critical range. In cases with little ambiguity or duplicity in the timing of petroleum system elements and processes, the critical range converges to one point, which is also the critical moment. The probabilistic framework introduces consistency to the critical moment estimation problem and quantifies the level of uncertainty in the estimation. This reduces the risk involved in petroleum exploration assessment.