Cook rice in 1 1/2 cups water as directed on package.
Meanwhile, heat oil in large skillet over medium-high heat until hot. Add garlic and mushrooms; cook about 4 minutes or until softened, stirring frequently. Add broth and thyme; bring to a boil.
Sprinkle chicken breast halves with salt and pepper; add to skillet. Reduce heat to medium-low; cover and cook about 10 minutes or until chicken is fork-tender and juices run clear, turning once.
In small bowl, blend cornstarch with 1 tablespoon cold water until smooth. Stir into chicken mixture. Increase heat to medium-high. Add sugar snap peas; cook about 5 minutes or until sauce is slightly thickened and peas are hot, stirring constantly. Serve chicken with sauce and vegetables over rice.