In a bowl, mix together 1/2 cup olive oil and the Herb & Spice No. 1.
Coat the chicken on both sides with the mixture and let sit out at room temperature while the grill preheats to 500°F.
Wash the broccolini and cut off the ends of the stems. Toss in a bowl with ¼ cup of olive oil and a pinch of the Spiced Fleur de Sel. Cut the lemons in half.
Place the chicken on the grill, skin side down. Cook for about 10 minutes and then flip the chicken over and add the broccolini and lemons (cut sides down) to the grill. Cook for another 10 minutes. Remove the chicken when the skin is crispy and the juices run clear. The broccolini and lemons are done when they are starting to char.