We did this simple BBQ chicken a few weeks ago. Since it wasn't a few days ago, I've since forgotten where I read about the specific cooking technique. For some reason, I don't recall seeing this exact approach for grilled BBQ chicken:
Use Indirect Heat for 100% of the cooking time
Almost all grillers know that direct heat and chicken doesn't work. But I don't recall a recommendation for 100% indirect heat. The approach I think I've seen most often is to char / brown first, then use indirect heat.
One key to this approach is that the chicken be coated in a dry-rub first. I used my own smoked paprika rub which is most frequently used for brisket.
Yes - you can / should brush a little sauce or even honey over the chicken at the last second and cook over high heat briefly.