Position a rack in the upper third of the oven and preheat to 475 degrees F. Pat the chicken dry and season with salt and pepper. Place skin-side up in a shallow baking pan and roast until the skin is golden brown and the chicken is cooked through, about 35 minutes.
Meanwhile, pulse the bacon, onion, mushrooms and rosemary in a food processor until finely chopped. Heat the olive oil in a large skillet over medium-high heat. Add the vegetable mixture and 1/4 teaspoon salt; cover and cook, stirring occasionally, until softened, about 8 minutes.
Puree the tomatoes in the food processor. Add the wine to the skillet and boil, uncovered, until almost completely reduced, 2 to 3 minutes. Add the pureed tomatoes and return to a boil. Reduce the heat, partially cover and simmer, stirring occasionally, until slightly thickened, about 20 minutes. Stir in the olives and brine and season with salt and pepper. Serve the chicken with the sauce.