(Preheat oven to 350.) Chicken: Purée garlic, juices, salt, and pepper in a blender until smooth. Put chicken pieces in a bag, pour purée over, massage to coat. Marinate in fridge, turning occasionally, 1 hour. Transfer to bowl reserving marinade. Heat oil and butter in 6-quart pot over med-high heat, then brown chicken in 2 batches, skin-side down, until skin well-browned about 6 minutes per batch. Transfer chicken to a plate, reserving fat in pot.

Rice: Sauté onions, peppers, and garlic in fat over high heat, scraping up brown bits from chicken, until softened. Add liquids, tomatoes (+ juice), reserved marinade, spices to vegetables and cook over high heat, stirring, 2 minutes.

Add chicken except breasts, skin sides up, simmer, covered, over low heat 10 minutes. Stir in rice, add breasts, arranging in 1 layer. Return to a simmer. Cover pot, transfer to oven and bake until rice is tender and most of liquid is absorbed, about 20 min.

Note: Prep liquid by simmering broth and spices. Add other liquids and set aside.