Prepare a hot fire in a charcoal grill or preheat a gas grill or broiler. Away from the heat source, lightly coat the grill rack or broiler pan with cooking spray. Position the cooking rack 4 to 6 inches from the heat source.
Arrange the tomatoes skin side down on the grill rack or skin side up on a broiler pan lined with aluminum foil. Grill or broil until the skins begin to blacken, about 5 minutes. Transfer to a bowl, cover with plastic wrap, and let steam until the skins loosen, about 10 minutes.
In a small frying pan, heat the olive oil over medium heat. Add the garlic and saute until softened, about 1 minute. Remove from the heat and set aside.
Core and peel the tomatoes. In a blender or food processor, combine the tomatoes, the garlic with the oil, and the vinegar. Pulse until well blended. Stir in 1 tablespoon of the basil and 1/8 teaspoon of the pepper.
Sprinkle the chicken breasts with 1/4 teaspoon salt and the remaining 1/8 teaspoon pepper. In a shallow dish, stir together the parsley, thyme and the remaining 2 tablespoons basil. Dredge the chicken in the herb mixture, coating completely. Grill or broil the chicken, turning once, until browned on both sides and no longer pink on the inside, about 4 minutes on each side.
Transfer the chicken breasts to warmed individual plates. Spoon the tomato sauce on top, dividing evenly. Serve immediately.