1. In a large, shallow baking dish whisk together the soy sauce, brown sugar, honey, and tomato paste. Remove 1/4 cup of the mixture; set aside. Add the chicken drumsticks and tenders to the remaining mixture in the dish. Turn pieces to coat with sauce. Cover and chill up to 8 hours.
2. Adjust grill for indirect grilling. Brush grill rack with oil. Test for medium heat over unlit side. Remove chicken drumsticks from dish; add to unlit side of the grill. Cover and grill for 35 minutes or until done (180 degrees F), turning and brushing with reserved glaze once. Remove the chicken tenders from the dish (discard remaining mixture in dish). Add to the lit side of the grill the last 8 minutes of grilling or until done (170 degrees F), turning and brushing once with glaze. Remove chicken from grill to a platter and serve.