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.