Season the chicken, inside and out, with 1 tablespoon of olive oil, the tarragon, 1/4 teaspoon salt and 1/8 teaspoon pepper. Toss the potatoes and onions with the remaining olive oil, salt and pepper.
When the oven comes to temperature, remove the skillet. After you remove the hot skillet from the oven, carefully place the chicken, breast side up, in the hot skillet. Surround it with the potatoes and onions.
TIP: Roasting the potatoes with the chicken juices makes them tender and flavorful and the small amount of chicken fat makes the potatoes golden and crispy. When the chicken is cooked and the potatoes are tender, remove the vegetables, tilt the chicken to check that the juices are clear. Drain chicken juices into the skillet. There should be just enough juices to serve au jus or make a pan sauce.