1. Process first 5 ingredients and 3 tablespoons jerk seasoning in a food processor 15 seconds or until blended, using the metal blade. Add mayonnaise, and pulse 5 times or until blended.
2. Rub mayonnaise mixture over chicken. Cover and chill 8 to 24 hours.
3. Light one side of grill, heating to 400° to 450° (high) heat; leave other side unlit. Sprinkle chicken with salt, pepper, and remaining 1 1/2 tablespoons jerk seasoning. Place chicken over unlit side of grill, and grill, covered with grill lid, 45 minutes to 1 hour or until a meat thermometer inserted into thickest portion registers 170°. Transfer chicken to a serving platter; cover loosely with aluminum foil, and let stand 10 minutes before serving.