In a medium saucepan with a tight-fitting lid, combine rice, 2 cups water, and 1/2 teaspoon salt and bring to a boil. Stir once, cover, and reduce heat to low. Simmer for 50 minutes. (Do not lift the lid or stir!) Remove from heat and let stand, covered, for 5 minutes; fluff with a fork before serving.
Meanwhile, heat the oil in a large skillet over medium-high heat. Season the chicken with 1/4 teaspoon each salt and pepper. Cook until browned, 4 to 5 minutes per side; transfer to a plate.
Add the onion, garlic, and 1/4 teaspoon salt to the skillet and cook, stirring occasionally, until tender, 4 to 6 minutes.
Add the broth, carrots, olives, and red pepper and simmer, covered, until the carrots are tender, 8 to 10 minutes.
Return the chicken to the skillet and cook until heated through, 3 to 5 minutes. Stir in the parsley and serve over the rice.