I learned some tricks from Cook's Illustrated over the summer, and they've definitely made my Barbecued Chicken better!
My favorite tip is this one: whether you are going to grill regular or skinless chicken parts, hit it with a rub at least 6 hours before grilling. I like to wait until way into the grilling before beginning to add the sugary barbecue sauce since it will tend to burn if left on too long. My new favorite rub is below.
Here's my other favorite tip: use a disposable aluminum pie pan or two, filled with water, underneath the grill grate on the cool end of the grill. When you cook your chicken lower and slower at the cool end (after searing it for flavor on the hot end of course), covered by the grill top, the added moisture does wonders for the meat.
Rub for barbecued chicken:
2 T brown sugar
4 t coarse salt
1 1/2 t onion powder
1 1/2 t garlic powder
1 1/2 t paprika
1/4 t ground cayenne pepper
Easiest to mix and apply in a plastic bag. Then refrigerate for at least 6 hours (in the bag is fine).