Add 1/2 tablespoon oil to a large nonstick skillet. Sauté garlic, red onion, and tomatoes in the oil for 2-3 minutes, or until the vegetables soften.
Mix black olives, red wine vinegar, oregano, and salt in with the vegetables and sauté for an additional 1-2 minutes, allowing the flavors to mix. Transfer tomato/black olive mixture to a small bowl and set aside.
Add remaining 1/2 tablespoon oil to the skillet. Place chicken in the skillet and sprinkle with salt and pepper, to taste. Cook chicken for 4-5 minutes on each side, or until fully cooked.
Serve each chicken breast with 1/4 cup tomato/black olive mixture and 2 tablespoons feta cheese.