1. Combine onions, jalapeño, garlic, ginger, salt, pepper, sugar and allspice in a food processor. Puree until smooth. Whisk orange juice, vinegar and soy sauce in a large measuring cup. Add juice mixture to food processor while motor is running; blend.
2. Place chicken in 2 large ziplock bags. Divide jerk mixture between bags and tightly seal them. Turn to coat drumsticks. Place in refrigerator and allow to marinate for at least 30 minutes or up to 24 hours.
3. Preheat a gas grill to medium. Remove drumsticks from bags and pat dry. Pour jerk mixture from ziplock bags into a small pan. Bring to a boil, reduce heat to low and simmer for 2 minutes. Oil grates and grill drumsticks about 6 inches from heat source, turning and brushing often with jerk mixture, until a meat thermometer inserted into thickest part of a drumstick reaches 170°F and chicken is no longer pink at the bone, about 40 minutes. Serve hot.