In a mixing bowl, combine the chopped basil, minced garlic, lemon juice, black pepper, garlic sea salt, paprika, crushed red pepper, and olive oil. Stir well to create a fragrant marinade.
Take your whole chicken and pat it dry with paper towels. Apply the marinade all over the chicken, including under the skin and inside the cavity. Let it marinate in the refrigerator for at least 2 hours, ideally overnight.
Preheat your smoker or grill for indirect cooking to about 225°F (107°C).
Place the marinated chicken on the grill grate, breast side up. Smoke for about 4 to 5 hours, or until the internal temperature reaches 165°F (74°C).
Remove the chicken from the smoker and let it rest for about 15-20 minutes before carving.