Position an oven rack 5 -to -6 inches from the broiler unit, and preheat the broiler. Line a rimmed baking sheet with foil. Toss the tomatoes, scallions and garlic on the baking sheet with 1 tablespoon oil until coated. Sprinkle with salt and pepper.
Broil until the vegetables are charred, flipping once, 10 to 12 minutes. Transfer to a cutting board to cool slightly. Switch the oven to bake at 350 F. Heat a large ovenproof skillet over medium-high heat and add 2 tablespoons of oil. Pat the chicken dry and sprinkle with salt and pepper. Lay the breast halves, smooth-side down, in the skillet and cook, flipping once, until golden on both sides, about 4 minutes per side. Transfer the skillet to oven and bake until the chicken just cooked through, 10 to 12 minutes.
While the chicken cooks, core the tomatoes, squeeze the garlic cloves from their skins, and chop them both with the scallions to make a chunky relish. Transfer the vegetables and all their juices to a bowl and stir in the remaining 1?4 cup oil, the vinegar, and the Worcestershire. Season with salt and pepper. Serve the chicken with the relish and toasted bread.
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