In a deep skillet or pot large enough to hold the chicken pieces, heat the oil over medium-high heat until just starting to smoke. Pat the chicken dry, season it with pepper, and place it in the hot oil. When the chicken is browned, turn it over and brown the other side. Set the chicken aside.
Very carefully, as it is very hot, pour out all but 2 tablespoons of the oil. Add the celery and the garlic. Over medium-high heat, lightly brown the garlic, but do not burn it, or it will taste bitter. Add the wine, chicken stock, vinegar, olives, and thyme. Raise the heat to high and bring to a boil. Reduce the liquid for 2 to 3 minutes. Add the chicken back. Add the butter and reduce, about 15 to 30 minutes. Check the sauce for seasoning and adjust with salt, pepper or vinegar.
Plate the chicken, drizzle with the sauce, and serve, garnished with thyme.
Recipe courtesy Ann Volkwein, The Arthur Avenue Cookbook : Recipes and Memories from the Real Little Italy, Regan Books, 2004 & Sal Biancardi of Biancardi Meats