Preheat the oven to 400 degrees. Pat the chicken dry and season with black pepper. Dredge in flour, shaking off any excess.
In a 12-inch ovenproof skillet or Dutch oven, heat 1 Tablespoon of the olive oil over medium heat. Add the chicken pieces in one layer and brown on both sides. Transfer to a plate and reserve.
If the pan looks dry, add a little oil. If it looks like there’s more than 2 Tablespoons oil, drain a bit off. Add the onions, cook over medium heat, stirring occasionally, until softened and lightly browned. Add the garlic and sea salt and cook until fragrant, about 1 minute.
Add the tomatoes, white wine, stock and cook, scraping any brown bits on bottom of the pan.
Arrange the thyme, olives and capers over the onion mixture. Place the browned chicken pieces side by side on top. Bring the mixture to a simmer. Cover and place in the oven.
After 15 minutes, baste the chicken with the juices in the pot. Continue cooking, uncovered, for an additional 30-40 minutes (depending on thickness), basting every 10 minutes if you have time. Sprinkle with parsley and serve. (You can also cook covered on the stove over low heat for 30 minutes.)