Whisk 1/3 cup of oil, 3 tablespoons of lemon juice, fennel seeds, 3/4 teaspoon salt, and 1/2 teaspoon pepper in a heavy-duty re-sealable 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 zest, 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. Grill the chicken until just cooked through, about 5 minutes per side. Transfer the chicken to plates. Drizzle the basil sauce over and serve.
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