Heat your entire grill to high. If using charcoal you'll want your grill to be as hot as possible.

Rinse and pat dry drumsticks.

Season your chicken generously. No need to be shy here, if for some reason you over season or use a flavor combination you don't care for, just remove the skin when you sit down to eat it.

Lubricate your grill with oil by using a well saturated piece of paper towel and grill tongs, or half an onion dipped in oil. Be careful of flames.

Arrange the chicken on one half of the grill. Do not over crowd.

Let it cook on the high heat for 3 minutes. Turn off the burners directly below the chicken, leaving the other half of the burners on high. The chicken will cook by indirect grilling.

If your grill is charcoal rake the coals to one side. Cook the chicken above the hot coals for 3 minutes then move the chicken to the other side of the grill. Make sure your grill vent is set for high heat.

Close the lid and leave the chicken alone for 30 minutes.

After 30 minutes flip the chicken, and rotate the chicken from the far side of the grill to be nearer to the flame or coals. You're not putting the chicken over the heat, you're just moving around the chicken on the one side of the grill.

Cook the chicken for an additional 15 minutes.

At this point it should be done, however check with a meat thermometer in the thickest part of the meat.

If it needs additional cooking time close the lid and check back in 5-10 minutes. If you'd like to speed up the cooking time you could finish the chicken over your heat source, but I highly recommend continuing with indirect grilling.