Preheat the oven to 400 degrees F (205 degrees C) and place a large, oven-safe skillet over medium-high heat.
Season the chicken all over with the salt and pepper.
Add the oil to the skillet and swirl to coat.
One shimmering, add the chicken, skin side down and allow it to sear for 5-10 minutes, or until the skin is brown. Flip and cook for 2-3 minutes on the other side. Remove to a platter.
To the hot pan, add the shallots and figs and sauté for 2-3 minutes or until the shallots are golden brown.
Add the olives, wine and thyme sprigs and boil for a minute or so, scraping up any browned bits that have stuck to the bottom of the pan.
Return the chicken to the pan, skin side up and place in the oven. Roast the chicken for 30 minutes, or until it reaches and internal temperature of 165 degrees F (74 degrees C).