Combine five-spice powder, salt, and pepper in a small bowl. Sprinkle mixture evenly over chicken. Place chicken on an oiled grill rack and cook for about 6 minutes per side, or until chicken is cooked through and has an internal temperature of 165 degrees F. Let chicken rest for 5 minutes.
Meanwhile, combine blackberry preserves, vinegar, and ginger in a nonstick skillet. Simmer over medium-low heat for about 8 minutes or until reduced to 1/2 cup.
Drizzle glaze over chicken and garnish with blackberries. Serve immediately.