Combine olive oil and butter in a sauté pan with a cover over medium heat. When butter is melted and begins to bubble, add smashed garlic cloves and chicken, skin-side down. Turn chicken, cooking until meat is browned on all sides and garlic is fragrant and well-browned. If garlic begins to burn, place it on top of the chicken.
Carefully add wine, then rosemary, salt, and pepper. Cover and cook for 30 minutes, or until chicken is cooked through.
Set chicken and garlic on a serving platter. Add water or white wine to pan and scrape the bottom to deglaze. Pour over chicken and serve with mashed potatoes or a simple side salad.