1. Preheat oven to 400 degrees. In a large Dutch oven or heavy pot, heat 1 tablespoon oil over high. Season chicken on both sides with salt and pepper. In batches, add chicken, skin side down, and cook until skin is golden and crisp, about 7 minutes. Flip chicken and cook 3 minutes more. Transfer chicken to a plate.

2. Pour off all but 1 tablespoon fat from pot and reduce heat to medium-high. Add onion and cook until translucent, about 5 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute. Add tomatoes and season with salt and pepper; cook until beginning to break down, about 3 minutes. Stir in vinegar and return chicken, skin side up, to pot; bring liquid to a boil. Transfer pot, uncovered, to oven and bake until chicken is cooked through, about 30 minutes.

3. Meanwhile, in a medium saucepan, heat 1 teaspoon oil over medium-high. Add carrots and cook until slightly softened, about 3 minutes. Add orzo, tossing to coat. Add 1 3/4 cups water and bring to a boil; reduce heat to low and cover. Cook until water is absorbed and orzo is tender, about 15 minutes. Remove from heat; fluff pilaf with a fork.

4. Reserve chicken breasts and half the pan sauce and refrigerate for later use. Serve chicken leg quarters with pilaf and remaining pan sauce.