Preheat oven to 375°.
Arrange chicken in a single layer in a 13 x 9-inch baking dish. Pour vinegar over chicken, and sprinkle with oregano, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Place garlic cloves in dish. Bake at 375° for 25 minutes, basting occasionally with pan drippings.
Remove garlic from dish, and peel. Place garlic in a bowl, and mash into a paste. Add buttermilk and next 6 ingredients (buttermilk through 1/8 teaspoon pepper); stir with a wire whisk until well-blended.
Cut each breast half diagonally across the grain into thin slices. Arrange 1 sliced breast half on each of 6 plates; spoon 1 1/2 tablespoons sauce over chicken. Garnish with thyme sprigs, if desired.