Season both sides of chicken breasts with 1/2 teaspoon of salt and 1/4 teaspoon of pepper. In a cast iron skillet, heat 2 tablespoons olive oil over medium heat. Add the chicken and cook until browned, about 10 minutes on each side. Remove the chicken from pan to a plate and set aside.
Add the remaining 1 tablespoon olive oil, onion, and garlic to the skillet and cook for 2 minutes, stirring frequently. Add the tomato sauce, diced tomatoes, chicken broth, cocoa, oregano, basil, sugar, 1/2 teaspoon of salt, and 1/2 teaspoon of pepper. Stir until well blended. Return the chicken to pan, cover and simmer for 15 minutes. Turn chicken over and continue cooking, covered for 15 minutes. Arrange the chicken on a serving platter and serve over rice.