Preheat the oven to 400˚F. In a small bowl, mix together the rub ingredients and set aside.
Wash and dry the chicken inside and out, removing and discarding any giblets from the cavity. Stuff the cavity with the lemon and onion quarters and sprinkle with the salt and pepper.
Spread the rub evenly all over the surface of the chicken. Place the chicken, breast side up, in a shallow roasting pan and arrange the halved potatoes all around the chicken. Drizzle the potatoes with the olive oil and toss to coat.
Bake in the preheated oven, basting the chicken and tossing the potatoes every 20 minutes or so, until the internal temperature of the chicken registers 165˚F and its skin is golden brown, approximately 1 hour and 20 minutes.
Remove the chicken from the oven and allow to rest for 5-10 minutes before carving. Serve family-style along with the roasted potatoes and a colorful, in-season vegetable, if desired.