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 butter in Dutch oven over medium heat.

Add slivered onion, carrot, and celery; saute 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 butter in a skillet over medium heat, and add pearl onions.

Saute 4 minutes or until tender; remove from skillet.

Add mushrooms, and saute 3 minutes.

Arrange the pearl onions and the mushrooms around chicken on serving platter, and spoon the sauce over chicken and vegetables.