Preheat oven to 500°F with oven rack in upper third.
Mash garlic into a paste with 1/2 teaspoon salt. Stir in oregano, red-pepper flakes, oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
Cut a 2-inch-long slit, about 1 1/2 inches deep, in side of each breast half and spread 1/2 teaspoon garlic mixture into each pocket. Coat chicken with remaining garlic mixture.
Roast chicken, skin sides up, in a shallow baking pan until just cooked through, 20 to 25 minutes.