Add the onion to the pan and cook, stirring often, until soft, 3 to 5 minutes. Add the garlic and cook 1 minute longer. Add the peppers and cook, stirring, until softened, about 3 minutes. Stir in the turmeric, cumin, rice, and 1/4 teaspoon salt. Stir until the rice is coated. Pour in the broth, and stir to distribute the rice evenly. Increase the heat to high and boil until liquid begins to be absorbed into the rice, about 2 minutes. Add the chicken to the rice. Cover and transfer the pan to the oven. Bake until the rice is tender and chicken cooks through, about 25 minutes.