Cut the chicken breasts in half, then season each side with sea salt, freshly cracked pepper, garlic powder, and dried oregano to taste.
In an ovenproof pan or cast-iron skillet, heat the olive oil over medium-high heat.
Once the cast-iron skillet is hot, add the chicken and cook for 3-4 minutes. Flip the chicken over, then add the crushed red pepper flakes, tomatoes, olives, capers, and anchovy to the skillet.
Place in the oven and cook until the chicken is cooked through, about 15-20 minutes.
Lay the cheese on top of each piece of chicken, then continue to cook for 2-3 minutes.