Preheat: Place a cast iron skillet in a cold oven. Pre-heat the oven to 425 degrees F. While the oven heats up, season the chicken.
Season: 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. Carefully place the chicken, breast side up, in the hot skillet. Surround it with the potatoes and onions.
Roast: Return the skillet to the oven and roast for 15 minutes at 425 degrees F. After 15 minutes, turn the oven temperature down to 370 degrees F and continue roasting for another 45 minutes, until the potatoes are tender, the chicken juices run clear, the legs move easily when wiggled and a meat thermometer inserted into the thickest part of a thigh registers 170 degrees F.
TIP: You can find all kinds of gourmet new potatoes at your local supermarket today. Try using baby Yukon Gold, Peruvian blue, or fingerling potatoes.
Serve: Remove the chicken and potatoes from the skillet and let it rest for 3 to 4 minutes before carving. Reduce the pan juices until slightly thickened and serve alongside.
TIP: You can also thicken your pan juices with 2 teaspoons of corn starch mixed with 2 tablespoons water. Add to your pan juices and bring it to a boil. Simmer until the desired thickness is reached.