For sauce, in a medium saucepan heat oil over medium heat. Add onion and garlic; cook about 4 minutes or until onion is tender, stirring occasionally. Stir in chili powder. Cook and stir for 1 minute more. Stir in cola, ketchup, chili sauce, brown sugar, vinegar, and Worcestershire sauce. Bring to boiling; reduce heat. Simmer, uncovered, about 15 minutes or until desired consistency, stirring occasionally.
For a charcoal or gas grill, place drumsticks from The Drumstick Cheat on the rack of a covered grill directly over medium heat. Grill for 13 to 14 minutes or until chicken is heated through and no longer pink (180 degrees F), turning once halfway through grilling and brushing generously with sauce during the last 5 minutes of grilling.