Ok; here's what I do.
I make sure the grill grate is hot and I brush it and use a paper towel dipped in vegetable oil with tongs and rub it over the grates before putting on the chicken. It also helps to dry the chicken skin with paper towel before putting it on the grill - do it before you season the chicken.
Another thing is to not move the chicken or flip it until its had a chance to cook a bit on the grates - using tongs, try wiggling the chicken pieces to see if they free up from the grates. Lastly, I start my chicken cooks using indirect heat. I'll finish the pieces over direct heat to give the skin some crispiness.
Hope this helps.