Drop pearl onions into boiling water in a Dutch oven, and cook 3 minutes. Drain; rinse with cold water, and peel. Set aside.
Melt 1 tablespoon of margarine in Dutch oven over medium heat. Add slivered onion, carrot, and celery; sauté 5 minutes. Place the onion mixture in a bowl; set aside.
Add chicken pieces to Dutch oven; cook 4 minutes, turning chicken pieces once. Cover, reduce heat to medium-low; cook 10 minutes. Combine flour, salt, and pepper; sprinkle over both sides of chicken. Cover and cook 5 minutes. Return onion mixture to pan; add wine and next 4 ingredients, stirring gently. Bring to a boil; cover, reduce heat, and simmer 25 minutes or until chicken is done. Remove chicken from pan, and arrange on a serving platter; set aside, and keep warm. Discard bay leaf.
Bring sauce to a boil; cook 7 minutes or until the sauce is reduced to about 3 cups, stirring occasionally. Reduce heat to medium; gradually stir in milk, and cook an additional 5 minutes, stirring occasionally. Remove from heat; cover and set aside.
Melt the remaining 2 teaspoons margarine in a skillet over medium heat, and add pearl onions. Sauté 4 minutes or until tender; remove from skillet. Add mushrooms, and sauté 3 minutes. Arrange the pearl onions and the mushrooms around chicken on serving platter, and spoon the sauce over chicken and vegetables.