Ok, let's talk technique. The key to properly cooking this cut of chicken is to use a zone temperature method. This is easiest with your gas grill, as you can more precisely control temperatures on different parts of the grill. Let's walk through this step by step...
Preheat one half of your grill on high heat and the other half on medium-low. Note, temperatures and times vary greatly because every grill is different!
Once the grill is properly heated, place the chicken breasts skin side down on the high heat side. This is where you want to have your squirt bottle and a watchful eye to knock down your flare-ups.
Grill the breasts skin side down for about 4 - 5 minutes with the lid open, you are mainly browning the skin in this step.
Using tongs, move the chicken breasts over to the cooler side of the grill and keep them skin side down.
Grill on the cooler side for about 6 - 7 minutes with the lid closed.
Open the lid and use your tongs to turn the chicken breasts over and move them back over to the hot side of the grill.
Cook the split chicken breasts bone side down on the high heat side of the grill for about 6 - 7 minutes with the lid open.
Using tongs, move the chicken back over to the cooler side of the grill and continue to grill bone side down for about 6 - 7 minutes longer with the lid closed.
If you are new to this, you may want to use an instant read meat thermometer to test the breasts. Shove that baby into the thickest part of the breast (without hitting a bone) and check for 160 degrees. If they need to cook longer, leave them on the cooler side of the grill with the bone side down and close the lid. Check them again every 6 minutes or so until done.
Remove the chicken from the grill, place on a plate and let the breasts rest for about 5 - 8 minutes before serving.
It may take a few experiments but once you get the technique down you will have a nice brown crunchy skin covering some delicious and juicy breast meat. If the skin gets burned a little, who cares? Peel the burnt skin off or cover them with some sauce and throw them back on the grill for a few minutes, making a glaze for what you claim you were planning on cooking in the first place, barbeque chicken!