Preheat oven to 375°

Place the chicken breasts on a baking sheet. Using your fingers, loosen the skin from the meat, leaving one side attached. Season the meat with salt and pepper.

In a fry pan, melt the butter with the olive oil. Add the leek and saute until softened. Remove the pan from the heat. Add the cheese and basil and stir to combine.

Divide the cheese mixture into 6 equal portions. Stuff 1 portion under the skin of each chicken breast. Pull the skin over as much of the meat as you can to help the chicken stay moist. Using your fingers, rub the chicken with olive oil and season generously with salt and pepper. Bake until the skin is lightly browned and the chicken is just cooked throught, 35 to 40 minutes.