The Business Process Modeling Notation (BPMN) is an emerging standard for capturing business processes. Like its predecessors, BPMN lacks a formal semantics and many of its features are subject to interpretation. One construct of BPMN that has an ambiguous semantics is the OR-join. Several formal semantics of this construct have been proposed for similar languages such as EPCs and YAWL. However, these existing semantics are computationally expensive. This paper formulates a semantics of the OR-join in BPMN for which enablement of an OR-join in a process model can be evaluated in quadratic time in terms of the total number of elements in the model. This complexity can be reduced down to linear-time after materializing a quadratic-sized data structure at design-time. The paper also shows how to efficiently detect the enablement of an OR-join incrementally as the execution of a process instance unfolds.