Heat oil in a large nonstick skillet over medium-high heat. Sprinkle chicken with 1/4 teaspoon salt and 1/8 teaspoon pepper. Add chicken to pan; cook 3 minutes on each side. Remove from pan. Add fennel; cook 5 minutes, turning to brown. Remove from pan. Add garlic; sauté 30 seconds. Add broth, vinegar, and 2 tarragon sprigs, scraping pan to loosen browned bits. Bring to a boil. Add fennel; cover, reduce heat, and simmer 7 minutes. Add chicken; cover and simmer 10 minutes. Remove chicken and fennel from pan, and keep warm.
Add 1/4 teaspoon salt, 1/8 teaspoon pepper, tomato, cream, and sugar to pan; bring to a boil. Cook until reduced to 1 cup (about 10 minutes), stirring frequently. Serve over chicken and fennel. Garnish with additional tarragon sprigs, if desired.