Mix beer, vinegar, chili, allspice, salt, pepper, and garlic in a zip top plastic bag or a shallow dish. Make sure marinade is well combined. Place drumsticks in bag and close tightly. Shake to coat all parts of drumsticks. Refrigerate for at least 1 hour, frequently flipping bag.
Take chicken out of bag, setting aside marinade. Lay chicken on a cooking spray coated broiler pan. Position under broiler for 20 minutes, flip a few times and baste with extra marinade. Chicken should be brown and crispy, serve immediately.