Heat oven to 400°F. Spray 2 1/2-quart casserole with cooking spray.
Melt butter in 2-quart saucepan over medium heat. Add rice; cook 2 minutes, stirring frequently. Add cooking sauce and 2/3 cup water. Heat to boiling; boil 1 minute, stirring occasionally. Stir in chicken and vegetables; heat to boiling, stirring occasionally. Remove from heat; stir in 1/3 cup of the cheese until well mixed. Cover tightly.
Bake 15 minutes. Stir rice mixture. Cover tightly; continue baking 15 to 20 minutes or until rice is tender and liquid is absorbed. Stir in remaining cheese.