Combine the first 4 ingredients in a small bowl to make the Seasoning Mix.
Blend the second 4 ingredients to make the marinade. Place the chicken in a large bowl, pour the marinade over the chicken, cover, and refrigerate at least 4 hours, but preferably overnight.
Preheat the broiler. Remove the chicken from the marinade and reserve the marinade. Place the chicken in a baking pan and broil until brown on both sides, about 7 minutes in all. Remove the chicken and set aside.
While the chicken is broiling, place the apple juice in a saucepan, bring to a boil, reduce to 1 cup, and set aside.
Preheat a heavy 5-quart pot, preferably nonstick, over high heat to 350o, about 4 minutes.
Add the onions, bell peppers, carrots, and 2 teaspoons of the Seasoning Mix, cover, and cook for 3 minutes. Add the garlic, mix in well, and scrape the bottom of the pot to clear it of all brown bits. Re-cover and cook 3 more minutes. Add the reduced apple juice and the remaining seasoning mix, scrape the bottom clear, and cook 4 minutes. Stir in the tomato sauce, diced tomatoes, stock, and reserved marinade. Add the chicken to the pot, bring to a boil, reduce the heat to medium, and cook until the meat is tender, about 20 minutes. Serve over the rice.