Hi M. ~
After years of cooking, I've found the best way to cook chicken on the grill is to first rinse the chicken very thoroughly in cold water.
Put the pieces into a large leakproof zip-loc type bag, and pour Italian dressing into the bag until all pieces are well coated.
Let it sit for as long as you want, but at least 1 hour before cooking (in the refrigerator).
Use a medium heat (too hot causes flame-ups) and cook the chicken until it tears away from the bone with a fork. Probably 30 minutes each side for cooking time.
If you use charcoal, be patient and wait for the coals to turn white before starting the chicken.
We've never had 'dried out' chicken since I've been cooking it this way....it browns on the outside and stays juicy inside, and the dressing doesn't really change the flavor! You can still add barbeque sauce the last 15 minutes if you want. Good luck!