1Heat gas or charcoal grill. In 1-quart saucepan, mix preserves, lime juice, chiles and adobo sauce. Heat over low heat, stirring occasionally, until preserves are melted. Stir in chopped cilantro; set aside. Sprinkle chicken with garlic-pepper blend, cumin and salt.
2Place chicken on grill over medium heat. Cover grill; cook 15 to 20 minutes, turning once or twice and brushing with half of the glaze during last 2 minutes of grilling, until juice of chicken is clear when center of thickest part is cut (at least 165°F).
3Heat any remaining glaze to boiling; boil and stir 1 minute. Serve chicken with glaze and fresh raspberries.