Heat gas or charcoal grill. In small bowl, mix brown sugar, paprika, cumin, garlic salt and chili powder. Rub both sides of chicken with seasoning mixture.
Place chicken on grill over medium heat. Cover grill; cook 8 to 10 minutes, turning once, until juice of chicken is clear when center of thickest part is cut (170°F).
Serve chicken with barbecue sauce.