DO-AHEAD TIP: Marinate chicken for 1 hour (see recipe).
Place chicken in a large zipper-topped plastic bag.
In a small bowl, combine next 7 ingredients (garlic through black pepper). Pour mixture over chicken then shake well and squish around to completely coat chicken. Refrigerate for 1 hour.
Preheat grill to MEDIUM. Bring chicken and marinade to room temperature. Lightly oil the grill grate. Remove chicken from marinade, shaking off excess (and discarding marinade and bag).
Grill chicken over indirect heat for 15 to 20 minutes, turning occasionally, until juices run clear. Watch carefully to prevent burning!
Top chicken with chopped pistachios and enjoy!