In a bowl, crush the canned tomatoes with your hands or a spoon until you have uneven 1-inch pieces. Mix in the anchovies, olives, capers, crushed red pepper, and 2 tablespoons of the chopped oregano. Set aside.

Season the chicken breasts with salt and black pepper. In a large skillet over medium-high heat, heat 2 tablespoons of olive oil until hot. Add the chicken and cook without disturbing for 3 minutes, or until browned. Turn and cook the other side for 3 minutes. Transfer the chicken to a plate.

In the same skillet over medium heat, heat the remaining 1 tablespoon of olive oil. Add the chopped garlic and cook, stirring, for 1 minute. Add the tomato mixture carefully (it may splatter) and cook for 1 minute until the splattering subsides. Stir well, reduce the heat, and simmer for 5 minutes. Taste and adjust seasoning as needed.

Return the chicken breasts and any accumulated juices to the skillet. Spoon some sauce over the top. Cover the pan and simmer for 5 to 8 minutes, or until a meat thermometer inserted into the thickest part of the chicken registers 165°F (74°C).

Serve the chicken directly from the skillet or transfer to a serving platter. Sprinkle the remaining 1 tablespoon of chopped oregano over the top and garnish with oregano sprigs. Serve with crusty bread if desired.