- Preheat the oven to 400 degrees F.
- Place the chicken breast between sheets of plastic wrap and pound, with the flat side of a meat mallet to 1/4-inch thickness. Pat dry with paper towels.
- Place 1 ball of mushroom stuffing along 1/2 of each chicken piece. Tuck the short ends in and, starting at 1 long side, roll up the chicken into a tight cylinder. Fasten with toothpicks. Season with salt and pepper.
- In a large, non-stick skillet, heat the oil over high heat. Add the stuffed chicken and cook, turning, until brown on all sides, 3 to 4 minutes. Remove from the heat and place in the oven. Bake until cooked through, about 7 minutes. Alternately, cover the skillet and cook over low heat until the chicken is cooked through, about 6 minutes.
- Remove from the oven. Transfer the chicken to a plate and cover to keep warm. Add the shallots to the pan juices and cook, over medium heat until soft, about 3 minutes. Add the garlic and thyme and cook, stirring, for 30 seconds. Add the Madeira and bring to a boil. Cook, stirring, until reduced by half, about 2 minutes. Add the chicken stock, return to a boil, and cook, until reduced by half, about 6 minutes.
- Add the chicken and any juices to the pan and cook until the chicken is warmed through, about 1 minute. Serve with Braised Celery.