I have always started my chicken skin side down. I find it to be a juicier bird and you get the crisp skin. You can also mop or season as it's cooking. Just when it's getting close to done, I flip to get some grill marks/color and finish it off. I have always had good results with this. i usually do this with a whole chicken, not halves. I split the bird at the breast and leave it intact at the spine. Pressing the bird flat I run a couple skewers through across the bird to keep it laying flat on the grill.
COS,Big Steel Keg,Ducane Gasser