The chicken: Heat a dry skillet on high for 1 minute, then add the oil. Season chicken with salt and pepper on both sides and add to the pan. Brown chicken, about 2–3 minutes per side, reducing heat to medium after 1 minute. Remove and pour out any dark oil.
The sauce: To the same skillet, add more oil and sweat the onions, 3–5 minutes (add more olive oil as needed). Add garlic, thyme, and bay leaf, followed by white wine. Reduce white wine until almost dry, then add tomatoes, season with salt and pepper, and toss. Add the chicken back to the pan, along with the olives. Cook 10 minutes, occasionally moving the sauce around until it thickens. Season to taste with salt and pepper.
Assembly: Spoon the sauce onto a serving platter. Remove the bay leaf and thyme. Add fresh oregano followed by chicken.