In small bowl, whisk together garlic, preserves, lime juice and soy sauce. Set aside 1/2 cup apricot mixture. Place chicken in large zip-top plastic bag; pour remaining apricot mixture over chicken. Seal bag; refrigerate 1 to 2 hours to marinate.
In medium bowl, mix brown sugar, pineapple juice, vinegar and allspice. Add nectarines, plums and cherries; toss to combine. Cover and refrigerate until ready to serve.
Prepare outdoor grill for direct grilling over medium heat. Remove chicken from marinade; discard marinade. Place chicken on hot grill rack and cook 18 to 20 minutes or until chicken loses its pink color throughout and internal temperature reaches 165