Place flour in a shallow dish; dredge chicken in flour.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add chicken; sauté 5 minutes, turning once. Remove chicken from pan, and keep warm.
Heat 2 teaspoons oil in pan. Add onion; sauté 3 minutes. Add rutabaga, turnip, squash, parsnip, and garlic; sauté 3 minutes. Stir in broth and remaining ingredients; nestle chicken into vegetable mixture. Bring to a boil; cover, reduce heat, and simmer 20 minutes or until chicken is done. Uncover and simmer 3 minutes or until thick. Remove bay leaf.