Preheat oven to 450. Season chicken with salt. Heat a large, heavy ovenproof skillet (preferably cast iron) over medium-high heat. Swirl in oil. Cook chicken, skin side down, until browned, about 5 min. Flip chicken, and push to side of skillet. All 1 cup stock and 1/2 teaspoon salt. Add potatoes to liquid. Bring to a boil. Add garlic, olives, lemon wedges, and thyme to liquid. Return to boil.

Transfer skillet to oven. Roast, stirring potatoes halfway through, until potatoes are tender and chicken is cooked through, about 30 minutes.

Return skillet to stove. Mix cornstarch with remaining 1/4 cup stock, and stir into pan. Bring to a boil to thicken sauce. Serve immediately.