Place the chicken breasts on a plate. Season them with salt and pepper. Sprinkle them with the chopped garlic and rosemary, turning once or twice to coat evenly. In a small bowl, whisk together 2 tablespoons of the oil and 1 tablespoon of the vinegar. Pour this over the chicken and set aside to marinate for 20 to 30 minutes. In a large, heavy skillet over medium-high heat, place the chicken breasts, skin side down. Reduce the heat to medium and cook for 8 minutes, or until browned. Turn the chicken over, cover the pan, and cook for 5 minutes. Remove the cover and continue cooking for 3 minutes, or until the chicken is cooked through.
Meanwhile, steam the spinach until barely wilted. Place 1 tablespoon of olive oil and the sliced garlic in a medium skillet and heat just until the garlic sizzles. Remove from the heat. Add the spinach and toss to coat.
Remove the chicken from the large skillet when cooked. Add the sugar and remaining 2 tablespoons of vinegar to the large skillet and boil, stirring until blended and reduced by half, about 1 minute. Drizzle a little of this glaze over each chicken breast. Serve on a bed of the cooked spinach.