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Put the chicken drumstick on the hottest part of the grill and cook them for 25 minutes, rotating them frequently with a pair of tongs to ensure even cooking. Step 5. Remove the chicken drumsticks from the grill and put them on a warm serving plate.
Chicken drumsticks can also be cooked at 375 degrees, but this will increase the cooking time to 45 to 50 minutes. Chicken should be placed with the skin facing up in a shallow roasting or baking pan. It can be seasoned first if desired, with olive oil and salt and pepper or other spice rub.