Preheat oven to 400°F.
Place chicken on cutting board. Cut a 3-inch deep pocket lengthwise in the thick side of each breast.
Place 2 basil leaves on each slice of mozzarella, sprinkle with salt and pepper. Stuff each breast pocket with a cheese bundle.
Wrap 2 slices prosciutto around each breast, anchoring with toothpicks.
Heat oil in large oven-proof nonstick skillet over medium-high. Add chicken and cook about 3 minutes on each side or until browned.
Transfer chicken in skillet to oven; bake 12 to 15 minutes or until done (internal temp 170°F).