PREHEAT OVEN TO 375F. Rinse the chicken pieces and pat dry. Sprinkle with desired salt and pepper and dust with flour, shaking off excess. Heat the oil in a large skillet over medium heat on the stove. Add chicken pieces, in batches, if necessary, without crowding the skillet, and brown on all sides until golden. Transfer the thighs and drumsticks to a large casserole or Dutch oven as they are done. Set the breasts aside. Add the Madeira, cream, bay leaves and thyme. Cover and place in the oven. After 10 minutes, add the liver and the breasts and replace in oven for another 25 minutes. When it's time to serve dinner, arrange chicken pieces on a serving platter and keep warm in the oven while finishing sauce. Remove bay leaves and thyme sprigs, pour sauce and livers into a blender or food processor and blend until smooth. Add salt as needed. Strain sauce into a saucepan, place over medium heat on the stove and add the grapes. Simmer for 2 minutes to heat the grapes. Remove the chicken from the oven, spoon sauce and grapes over it and serve immediately.