1) Whisk 80ml of oil, three tablespoons of lemon juice, fennel seeds, 3/4 teaspoon of salt, and 1/2 teaspoon of pepper in a resalable plastic bag. Add the chicken and seal the bag. Massage the marinade into the chicken. Refrigerate at least 30 minutes and up to one day, turning the chicken occasionally.
2) Blend the basil, garlic, lemon zest, remaining lemon juice, 3/4 teaspoon salt, and 1/2 teaspoon pepper in a blender until smooth. Gradually blend in the remaining oil. Season the basil sauce, to taste, with more salt and pepper, if desired.
3) Prepare the barbecue for medium-high heat or preheat a griddle pan over medium-high heat. Remove chicken from the marinade. Discard the marinade. Grill the chicken until just cooked through, about 8 minutes per side. Transfer the chicken to serving plates, drizzle with the basil sauce and serve.