In a large heavy skillet or pot, heat 1 tablespoon of the oil over moderate heat until hot. Add the onions and thyme and cook for 5 to 6 minutes, or until lightly browned. Transfer browned onions to a bowl. In the skillet heat the remaining 2 tablespoons oil over moderately high heat until hot. Pat the chicken pieces dry and season with salt and pepper. Brown the chicken, in batches if necessary, and transfer to a plate.
Drain off all but 2 tablespoons of fat from the pan and add the shallots and garlic, cooking over moderate heat for 30 seconds. Stir in the tomatoes, wine, and cheesecloth bag and add the onions, chicken skin side up, and any juices that have accumulated on the plate. Bring the liquid to a boil, simmer the mixture, covered partially, for 20 minutes. Simmer the mixture, uncovered, for 15 minutes, or until the breast pieces are tender, and transfer the breast pieces to a plate. Simmer the remaining chicken and onions for 15 minutes more, or until they are tender, transfer them to the plate, and discard the cheesecloth bag. Cook the sauce over moderately high heat, stirring, for 10 to 15 minutes, or until it is thickened, add the chicken, onions, olives, and lemon juice and cook the stew, covered, over very low heat for 3 minutes, or until it is heated through.
The stew may be made 1 day ahead. Let the stew cool, uncovered, and chill it, covered. Reheat the stew, covered, over low heat, adding water if necessary.
Recipe courtesy of Gourmet Magazine