Pour a generous amount of olive oil into a skillet and arrange the chicken pieces in the pan. Add the garlic cloves and the rosemary sprig.
Place the skillet over medium heat and brown the meat thoroughly, turning the pieces to ensure they become golden on both sides.
Once the chicken is nicely browned, deglaze with the white wine.
Season with salt and pepper, then add the remaining ingredients: the green and black olives, tomatoes, and capers. Stir well and cook for another couple of minutes.
Cover with a lid and let cook for about 30 minutes, turning the chicken occasionally.
Serve the Mediterranean chicken on a serving platter, spooning the pan sauce and toppings generously over the meat.