The turbine coolant collection/distribution chamber, as an important component of the secondary air system, undertakes the task of collecting and distributing coolant for guide vanes. To improve the outflow uniformity and reduce the flow loss, a multiobjective optimization method is developed for geometric parameters of turbine chamber. Numerical experiments were designed by Latin hypercube sampling and solved by the CFD method. Based on these data sampling, least square support vector machine (LS-SVM) was used for the surrogate model, and a kind of chaotic optimization algorithms was used for searching for the Pareto solution set. The results show that the streamline change in the optimized chamber is smoother, and the jet impingement effect of the coolant from the inlet tube was significantly weakened. At the condition that each goal has the weight of 0.5, the optimized discharge coefficient increases by 26%, and the outflow nonuniformity decreases by 79% compared with reference structure.