Rosemary Chicken with Tomatoes and Olives

Preheat oven to 375°F. Season chicken with salt and pepper. Heat a large ovenproof straight-sided skillet or braiser over medium-high. Swirl in oil. Working in two batches if necessary, add chicken, skin-sides down, and cook, undisturbed, until golden brown and crisp, 6 to 8 minutes. Flip and brown other sides, 4 to 5 minutes more. Transfer to a plate; drain all but 2 tablespoons fat from skillet.

Reduce heat to medium. Add garlic, capers, anchovies, rosemary, and red-pepper flakes to skillet. Cook, stirring occasionally, until fragrant, about 1 minute. Add tomatoes and broth; bring to a simmer, scraping any browned bits from bottom of skillet. Continue to simmer until thickened slightly, about 10 minutes. Season to taste. Return chicken to skillet, skin-sides up, along with any accumulated juices and olives.

Transfer skillet to oven and braise, uncovered, until chicken is cooked through and liquid is reduced to a thick gravy, 40 to 45 minutes. Remove and discard rosemary. Serve over mashed potatoes or polenta.