Heat gas or charcoal grill. In food processor or blender, process all ingredients except chicken pieces until smooth. Reserve 1/3 cup preserves mixture.
Place chicken pieces on grill. Cover grill; cook over medium heat 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). Before serving, brush with reserved preserves mixture.