1Heat gas or charcoal grill. In food processor or blender, process all ingredients except chicken pieces until smooth. Reserve 1/3 cup preserves mixture.
2Place chicken pieces on grill over medium heat. Cover grill; cook 25 to 30 minutes, turning frequently and brushing with preserves mixture during last 15 minutes of cooking, until juice of chicken is clear when thickest piece is cut to bone (170°F for breasts; 180°F for drumsticks). Discard any remaining preserves mixture used for brushing.
3Before serving, brush chicken with reserved preserves mixture.