Whisk together vinegar, egg, butter, olive oil, and spices.
Remove 1/2 cup of mixture.
Add chicken drumsticks to remaining marinade.
Cover and refrigerate for at least 2 hours.
Remove chicken from marinade.
Grill chicken drumsticks on a grill preheated to 450 degrees, about medium high heat, flipping ever 5 - 7 minutes, using reserved marinade to baste chicken.
Grill chicken for about 30 - 35 minutes or until internal temperature is 185 degrees.