Preheat oven to 350 degrees F (175 degrees C).
Cook white rice in water and butter over medium heat until tender, about 10 minutes. Stir in instant rice and continue cooking for 2 minutes.
In a large skillet, heat olive oil or butter over medium-high heat. Add onion and garlic, and cook until softened. Add chicken and vegetables, and cook until chicken is no longer pink.
Spread rice mixture into a 9x13 inch baking dish. Pour chicken mixture over top, and sprinkle with cheddar cheese.
Bake for 20 minutes, or until cheese is melted and bubbly.