Preheat the oven to 375 degrees.
Place the chicken breasts on a baking sheet. Loosen the skin from the meat with your fingers, leaving one side attached.. Cut 12 thick slices of the Montrachet and place 2 slices plus a large basil leaf under the skin of each chicken breast. Rub each piece with olive oil and sprinkle generously with salt and pepper. Bake the breasts for 35 to 40 minutes, until just cooked through. Serve hot or at room temperature.
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