Preheat the oven to 425°F.
In a small bowl, mix together the olive oil, tarragon, lemon juice, garlic, salt, and pepper.
Rub the herb mixture all over the chicken, including under the skin for extra flavor.
Stuff the cavity of the chicken with the quartered lemon and onion.
Place the chicken breast-side up in a roasting pan and pour the chicken broth around the base.
Roast in the preheated oven for 1 hour to 1 hour 15 minutes, or until the internal temperature reaches 165°F and the juices run clear.
Let the chicken rest for 10-15 minutes before carving.