Preheat the oven to 450 degrees. In a small roasting pan, scatter the shallots, carrot and celery in an even layer.
Rub the chicken with 2 tablespoons of the olive oil, then generously season with salt and black pepper. Arrange the chicken skin-side up on top of the vegetables in the pan. Sprinkle the rosemary, thyme and 1 tablespoon of the basil over the chicken.
Roast until an instant-read thermometer inserted in an inner thigh registers 165 degrees F, about 35 minutes. The skin should be golden brown and the juices should run clear.
Meanwhile, in a small skillet, heat the remaining 1 tablespoon of olive oil over moderately high heat. Add the garlic and cook, stirring, until golden brown, about 45 seconds. Add the tomatoes, red pepper and vinegar; season with salt. Cook, stirring frequently, until the tomatoes are softened, about 3 minutes. Transfer to a serving bowl, stir in the remaining 2 tablespoons of basil and season with salt and pepper. Serve the tomatoes with the roast chicken.