Sprinkle chicken with salt and black pepper. Place in large resealable plastic bag set in shallow dish. For marinade,in bowl combine half of the nectar, 2 tablespoons of the preserves, half of the mint, 1 tablespoon of the olive oil, the vinegar, curry, and garlic. Pour over chicken. Seal bag; turn to coat. Refrigerate 2 to 4 hours.
Remove chicken from marinade; discard marinade. For charcoal grill, place chicken on rack directly over medium coals. Grill,uncovered, for 12 to 15 minutes or until chicken is no longer pink (180 degrees F), turning once halfway through. Add apricots to grill, cut sides down, the last 5 minutes of grilling or until lightly browned. (For gas grill, preheat grill. Reduce heat to medium. Place chicken on grill rack over heat. Cover; grill as above.)
For sauce, in bowl combine remaining apricot nectar, preserves, mint, olive oil, the chopped green onions, 3 tablespoons of the pistachios, the mustard, mustard seed, and 1/4 teaspoon salt. Serve chicken with sauce and apricots; sprinkle with remaining pistachios. Makes 4 servings.