Rinse rice well with cold water and drain. Add to a medium pot with water and bring to a boil. Cover and cook for 30 minutes or until water has evaporated. Set aside.
In the meanwhile, preheat non-stick skillet on low-medium heat and swirl oil to coat. Add onion, garlic and mushrooms; cook for 5 – 7 minutes or until translucent and fragrant, stirring occasionally. Transfer to a large bowl along with rice, chicken, 1/2 cup tomato sauce, balsamic vinegar, oregano, salt and pepper; mix well with your hands.
Preheat oven to 400 degrees F. Fill each bell pepper 3/4 full with meat and rice mixture; place in a heavy bottom pot/pan with a lid or a dutch oven. Place pepper tops in between (do not throw them out!).
In a small bowl, mix water and remaining tomato sauce and pour over peppers and some at the bottom of a pan. Cover with a lid and bake for 40-60 minutes, depending how tight your lid fits (mine didn’t so it took 60 minutes for me). Remove from the oven and serve hot with plain yogurt and whole wheat bread, if desired.