Pat the chicken dry and season both sides with kosher salt, ground black pepper, Italian seasoning, and half of the dried oregano.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Sear the chicken 3–4 minutes per side until golden brown, then transfer to a plate and drizzle with lemon juice.
Add the remaining 1 tablespoon olive oil to the same skillet. Add the minced garlic and chopped anchovy fillets and sauté about 1 minute, until the garlic is fragrant and anchovies begin to break down.
Add the can of whole peeled tomatoes with their juices and use a spoon to crush them into uneven pieces. Stir in the red pepper flakes, chopped Kalamata olives, capers, and remaining dried oregano.
Bring the sauce to a simmer and cook 8–10 minutes until it thickens slightly.
Return the seared chicken to the skillet, nestle into the sauce, cover, and simmer about 10 minutes more until the chicken reaches 165°F (74°C) internal temperature.
Remove from heat, sprinkle with chopped fresh parsley, and serve warm.