Season shrimp with basil, salt, and cayenne pepper. Add shrimp to the bowl, and stir until evenly coated.
Cover, and refrigerate for 30 minutes to 1 hour, stirring once or twice.
Heat grill to medium; lightly oil grill grate.
Thread shrimp on skewers; pierce once near head and once near tail. Place shrimp on preheated grill.
Cook 2-3 minutes per side or until opaque.