1. Bring the grill to a temperature of 350F ( at 400 it will flame the grill up)
2. once u have oiled the grill, add the leg quarters face down with skin on and close the lid. 
3. if the flame burns on it just move the chicken to a part where theres no flame. 
4. Switch off one burner and keep the other burning. 
5. After 3 minutes move the chicken to the part of the grill where the flame is not on- it will cook in indirect heat now.
6. the trick with perfectly juicy chicken is cooking it in indirect heat till the temperature reaches 170-175F( you will need a digital thermometer for perfect chicken-it is absolutely obligatory:))
7. turn the chicken over just ONCE and baste it once more with oil somewhere after 15-20min.
8. remove chicken after 45 min

http://eatthiscooking.blogspot.com/2007/09/how-to-... How To Make It: 1. Prepare the grill for medium heat. It would be wise to use a thermometer to get a reading of 325-350 degrees. 2. If you are using a gas grill, only turn on one side of the grill burners. If you are using a charcoal grill, mound up the coals on one side. The reason for this is because you will be incorporating both direct (meat over the heat source) and indirect (meat away from heat source) cooking techniques. 3. Brush both sides of the chicken leg quarters with the olive oil and season with the salt and pepper. 4. Place the chicken directly over the heat and grill with the lid open for about 3 minutes per side. (It doesn't make a difference which grill you are using here as long as you have an internal temperature of 325-350 degrees.) 5. Move the chicken to the other side of the grill (away from the heat source) and grill with the grill lid down for about 45 minutes, or until a thermometer inserted into the thickest portion of the chicken leg quarter registers 170 degrees. Although salmonella, a bacterium that causes food poisoning, is instantly killed at 165 degrees, chicken still has a slight pink color at that temperature and most people are hesitant to eat chicken that is pink. Therefore, 170 degrees is what I recommend. (On a side note: if you prefer to cook legs or thighs, use the same techniques described above. Just reduce the covered grilling time to about 30 to 35 minutes or until a thermometer registers 170 degrees.) 6. Once this is accomplished, your chicken has just been grilled to perfection. Now there's just one more step to take and that is, 7. Bring in the chicken, serve it to the awaiting fortunate recipient(s) and bring on the accolades.