Combine flour, 1/8 teaspoon pepper, and 1/8 teaspoon salt in a shallow dish. Dredge chicken in flour mixture.
Heat oil in a large Dutch oven over medium-high heat. Add chicken and shallots. Cook 5 minutes, and brown on all sides. Remove chicken. Add mushrooms; sauté 3 minutes. Add tomato, carrot, celery, tarragon, and bay leaf. Cook 1 minute, stirring constantly. Stir in wine and broth; scrape pan to loosen browned bits. Return chicken to pan, and bring to a boil. Cover, reduce heat, and simmer 1 hour, stirring occasionally. Stir in 1/8 teaspoon pepper and 1/4 teaspoon salt. Garnish with chives.