In this paper, a class of chance constrained multiobjective linear programming model with birandom coefficients is considered for vendor selection problem. Firstly we present a crisp equivalent model for a special case and give a traditional method for crisp model. Then, the technique of birandom simulation is applied to deal with general birandom objective functions and birandom constraints which are usually difficult to be converted into their crisp equivalents. Furthermore, a genetic algorithm based on birandom simulation is designed for solving a birandom multiobjective vendor selection problem. Finally, a real numbers example is given. The paper makes certain contribution in both theoretical and application research related to multiobjective chance constrained programming, as well as in the study of vendor selection problem under uncertain environment.