Summary: The safety and efficiency of free flight will beneflt from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is needed, therefore, of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method to estimate that conflict probability is presented. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single, equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and a Monte Carlo validation are presented.