1. Preheat oven to 350°. Wrap sweet potatoes in foil, and bake at 350° for 45 to 50 minutes or until soft when squeezed. Remove from oven, and set aside.
2. Rinse chicken, and pat dry; remove any excess skin or fat. Sprinkle all over with sea salt and pepper. Heat 1 tablespoon oil in a large ovenproof skillet over medium heat, and add chicken, breast side down. Cook until skin is crispy and brown, about 10 minutes. Turn chicken over, add garlic and shallot, and cook, stirring constantly, about 1 minute. Add vinegar, wine, and broth; stir, scraping up all browned bits from bottom of pan. Stir in lentils, and add more sea salt and pepper.
3. Transfer skillet to oven, and bake at 350° for 40 to 45 minutes or until lentils are tender and juices from chicken thighs run clear or meat thermometer registers 170°.
4. Peel reserved sweet potatoes, and mash with a potato masher. Sprinkle with sea salt and pepper. Cut chicken into 8 serving pieces. Place a spoonful of sweet potato on each plate, and top with lentils, shallots, and a piece of chicken. Spoon cooking liquid over and around chicken and vegetables. Sprinkle with tarragon. Serve warm.
*For ease, ask a butcher to do this for you.
**You can substitute regular brown lentils, but the French green variety has more depth of flavor.