In 2-quart saucepan, heat wild rice, broth and water to boiling over high heat. Reduce heat to low. Cover and simmer 45 to 60 minutes or until rice kernels are open and almost tender; drain if necessary. Stir in thyme. Spread rice in ungreased 9x9-inch glass baking dish.
Heat oven to 350°F. In 12-inch skillet, heat butter over medium-high heat. Cook chicken in butter 8 to10 minutes, turning once, until brown. Place on cooked rice. Add mushrooms to skillet. Cook 3 to 5 minutes, stirring occasionally, until lightly browned. Stir in bell peppers and Alfredo sauce; pour over chicken.
Bake uncovered 45 to 55 minutes or until mixture is bubbly and juice of chicken is no longer pink when centers of thickest pieces are cut.