Pat the chicken breasts dry with paper towels and season both sides generously with salt and pepper.
Heat the skillet over medium-high heat and add olive oil, swirling to coat the bottom.
Place the chicken breasts in the skillet and cook undisturbed for about 5-6 minutes until the edges are golden brown and the underside releases easily from the pan.
Flip the chicken and cook for another 5-6 minutes until fully cooked through, with an internal temperature of 165°F (74°C), and the exterior is golden and crispy.
Reduce heat to medium-low, then top each chicken breast with slices of mozzarella, a few basil leaves, and a slice of prosciutto. Cover the skillet with a lid or briefly transfer to an oven to melt the cheese and warm the prosciutto until the mozzarella is gooey and bubbling, about 2-3 minutes.
4 pieces chicken breasts
Remove from heat, drizzle with balsamic glaze if desired, and serve immediately, garnished with additional basil leaves for color.
4 pieces chicken breasts