Put the chicken in an ovensafe baking dish. Drizzle with 2 tablespoons of the olive oil and sprinkle with salt and pepper. Use tongs to turn the chicken and evenly coat. Bake for 15 minutes until browned but not cooked all the way through (it will finish cooking with the rice).
Meanwhile, add the remaining tablespoon olive oil to a large saucepan over medium-high heat. Add the rice and stir to coat.
Toast the rice, stirring occasionally, until it is lightly golden, about 2 minutes. Stir in the onion and garlic and continue cooking until the rice is just lightly browned and the vegetables are starting to soften, about 2 minutes more. Make sure the garlic does not brown.
Add the tomato sauce, cumin, garlic powder, onion powder, bouillon and 3 cups water. Stir to combine. Bring to a gentle boil, then reduce to a simmer and add the chicken to the rice in an even layer, skin-side up and not overlapping. Cover and cook until the rice is tender and the chicken is cooked through, about 20 minutes.