Preheat oven to 450 degrees. Coat large, heavy nonstick roasting pan with olive oil cooking spray.
Toss root vegetables with vinegar, 2 teaspoons tarragon, 1/2 teaspoon thyme, garlic, salt, black and red pepper until coated. Bake in preheated oven 30 to 45 minutes, until vegetables begin to caramelize.
Add green beans. Bake 10 to 15 minutes longer, until vegetables are tender.
Remove vegetables to large bowl. Cover to keep warm.
And wine to pan, scraping brown bits off bottom. Add chicken. Bake 15 to 20 minutes until cooked through. Add chicken to vegetables. Cover.
Place roasting pan on top of range. Add broth. Bring to simmer.
Stir flour with 1/2 cup water until smooth. Add to broth. Cook, stirring constantly, until smooth.
Add 1 teaspoon tarragon and 1/2 teaspoon tyme. Return vegetables and chicken to pan. Toss to coat evenly. Heath through.