The paper proposes a chance-constrained stochastic model predictive control strategy to handle autonomous vehicle interactions with pedestrians near unsignalized crosswalks in a safe and efficient manner. The strategy is designed to account for inherent uncertainties of pedestrian crossing behavior, and the effect of the vehicle state on pedestrian decisions. Probabilistic constraints are introduced within the optimal control problem to facilitate pedestrians’ understanding of vehicle intentions and thus to avoid safety-critical situations. Finally, the proposed strategy is verified against a baseline control strategy via simulations of pedestrian model developed by using experimental data, for a variety of initial conditions and levels of pedestrian behavior uncertainty.