2. Cut a deep horizontal pocket in the side of each chicken breast. Make the pocket as large as you can without piercing the top or bottom of the breast. Place an equal amount of goat cheese and about 4 basil leaves in the pocket of each chicken breast. Secure the pocket with toothpicks threading along the side to close.
3. Heat the oil in a heavy oven-proof skillet until it begins to smoke. Cook each side of the chicken until golden brown.
4. Add the vinegar and chicken stock and bring to a boil. Lower the heat and gently simmer the chicken for 2 or 3 minutes per side until cooked through.
5. Remove the chicken breasts from the skillet and keep warm. Continue to cook the sauce until it is reduced to a thick syrup.
6. Taste the sauce and and season with salt and pepper. Spoon the sauce over each chicken breast.