Dry the chicken with paper towels. In a large (8- to 9-quart) Dutch oven, heat the oil over medium-high. Lay in the chicken in a single layer and brown on all sides; remove.
Reduce the heat to medium, scoop in the onions and cook, stirring regularly, until nicely golden, about 7 minutes. Add the tomatoes and chiles, cover and cook 5 minutes. Uncover and cook until thick and very reduced (it'll be as thick as tomato paste). Add the spices, olives, capers, brine, raisins and 3 cups water.
When the mixture returns to the boil, nestle in the breasts, partially cover and cook 20 minutes, until the meat is cooked clear to the bone. Taste and season with salt, spoon everything into a warm, deep serving platter, sprinkle with a few extra olives and capers, then carry to the table.