This wasn't really tarragon chicken, since we didn't have any tarragon. According to the internet you can use anise or fennel seed as a replacement. We used some anise seed. It was very good.
1 cup all-purpose flour
1 tsp salt
1/2 tsp pepper
8 chicken thighs (we use 4 chicken breasts cut in half)
3 tbs olive oil
1 1/2 cup chicken broth
1 tbs fresh tarragon or 1 tsp dried (or 1/2 tsp anise seed, slightly crushed)
1 cup sliced mushrooms
2 1/2 tbs lemon juice (we used 1 lime instead)
Combine flour, salt and pepper in a shallow bowl. Coat chicken in flour, reserving remaining flour mixture. Heat oil in a deep 12-inch skillet over high heat.
Add chicken to skillet. Cook until browned on both sides, about 3 minutes on each side. Stir in 2 tbs reserved flour mixture into pan drippings.
Add broth gradually to skillet, stirring continually. Stir in tarragon (or anise). Bring to a boil; reduce heat. Simmer, covered for 10 minutes.
Add mushrooms to skillet. Simmer until chicken is cooked through, about 10 minutes. Stir in lemon (lime) juice. Serve immediatley.
Since we used breasts instead of thighs, we didn't have much for pan drippings, so I added the broth first then the flour mixture so the flour wouldn't burn.