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.
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.
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.
Reserve chicken breasts and half the pan sauce and refrigerate for later use. Serve chicken leg quarters with pilaf and remaining pan sauce.
Wrap up and refrigerate the extra chicken breasts and sauce you make tonight and use for a quick dinner later in the week.