Preheat the oven to 450 degrees . Place the chicken breast side down on a work surface. Using kitchen shears, cut along both sides of the backbone; pull out and discard. Open the chicken like a book and flip skin side up. Press on the breast until the bone cracks. Pat dry.
Place a large, ovenproof skillet over medium-high heat until hot. Rub the chicken all over with 1 1/2 teaspoons olive oil; season well with salt and pepper. Place the chicken breast side up in the skillet; transfer to the oven and roast until the skin is crisp and golden and an instant-read thermometer registers 165 degrees when inserted into the thigh, 40 to 45 minutes. Let rest for 5 minutes before carving.
Meanwhile, spread the bread cubes on a baking sheet; toast until lightly golden, 10 to 12 minutes.
In a large bowl, combine the tomatoes, onion, parsley, garlic, remaining 3 tablespoons olive oil and the vinegar; season with salt and pepper. Add the bread cubes and toss. Serve the chicken on top of the bread salad.