Patting dry and then air drying on a rack helps significantly.
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I agree with this, made a big difference for me last time I did split breasts and thighs bone in and especially when doing whole birds. I also, do a bit of butter basting during the cook, tends to help crisp the skin.
I actually take the chicken the night before my cook, wash it in the sink then dry it with paper towels - inside and out. Trim up anything you feel needs trimming. I then add kosher salt and put it in the fridge uncovered until the next day when I want to cook it. Just before adding to the grill, light rub/pat on some olive oil and no-salt BBQ rub (already has salt from the dry brine.) After a couple hours it may start to look dry, a light - stress light- butter baste can help keep it from drying out and aid in the crispy skin goal.
Other times, I'm lazy and just take it out, wash/rinse it, pat down well to get it as dry as I can and then add olive oil/rub and put her on the grill. Either way, getting the bird dry first and then a butter baste or two during the cook has never steered me wrong - on a gasser, charcoal, hot/fast or low/slow. Even in the oven I do it almost the same way.