Whisk 1/3 cup of oil, 3 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 1 day, turning the chicken occasionally.

Meanwhile, blend the basil, garlic, lemon peel, remaining 1/4 cup lemon juice, 3/4 teaspoon salt, and 1/2 teaspoon pepper in a blender until smooth. Gradually blend in the remaining 1/3 cup oil. Season the basil sauce, to taste, with more salt and pepper, if desired.

Prepare the barbecue for medium-high heat or preheat a grill 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.