For the roasted Jerusalem artichokes and chicken breast: Place the chicken and pineapple juice in a baking dish. Marinate for a minimum of 30 minutes in the refrigerator, or a maximum of 24 hours.
Preheat the oven to 350 degrees F.
Heat the oil in large cast-iron pan over medium to high heat. Once the oil is hot, add the Jerusalem artichokes to the pan and sprinkle with salt and pepper. Cook the Jerusalem artichokes until golden brown, about 3 minutes. Turn the Jerusalem artichokes over and cook until golden brown, about 3 minutes. Remove from the pan and set aside. Add the chicken to same hot pan, skin-side down. Once the skin is crisp, golden and lightly charred, about 4 minutes, flip over. Add the reserved Jerusalem artichokes to the pan and place in the oven until the chicken is cooked through and reaches an internal temperature of 165 degrees F on an instant-read thermometer, about 25 minutes. Remove from the oven and allow the chicken to rest for 10 minutes before slicing.
For the Jerusalem artichoke nicoise salad: Place the roasted Jerusalem artichokes and the green beans on a plate. Scatter the tomatoes, onions and olives over the green beans and Jerusalem artichokes. Place the sliced chicken breast in the center. Place the hard-boiled eggs around the chicken. Whisk the olive oil, lemon juice, salt and pepper in a bowl. Drizzle over the salad and serve.