Do you have rocks or heat shield?

I had a same problem with my charbroil. When my wife and I bought my first house, we did not have a lot of money and the old grill was on it last legs. I bought a 35000btu charbroil with a heat shield from Home Depot. A cheap grill to get us buy for a few years. The sound of the gas burning sounded like a steel cutting torch I used in the shipyard. The heat was just blowing by. I bought some lava rocks around the bottom of the grill as high I could stack them. This seems to slow the incoming air from the bottom. I am getter better results. Though I still use a meet thermometer check the chicken.

Are you letting the chicken cook little before put the BBQ sauce on? The sugars in the sauce will burn long before the chicken will start cooking.

Anybody else having the same problem with the cheap charbroils?

Try two techniques:

1. Brine your chicken first. Basically, make a salt water solution and soak your chicken in a big ziplock bag for about an hour, then rinse and pat dry with paper towels. Look up brine recipes on the net - it's super easy. This will help keep your meat moist during the grilling process.

2. Assuming your gas grill has at least two temperature zones to control, turn one side on, leave the other completely off. On the on side, turn it up to medium high and brown the outside of your chicken pieces - don't walk away, pay attention to them and turn them after just a couple of minutes. That takes care of the outside. Then move them to the side with no fire on, then cover all the chicken with an upside down disposable alumininum roasting pan, so that it covers the chicken and reaches over a little bit of the side of the grill which does have the fire on (reduce to medium heat). You're basically creating a tiny oven to evenly cook the chicken which helps get the insides cooked. You could omit the pan and just close the grill cover, but that will take longer and every time you open the cover, it takes longer to heat back up when you close it. "If you're lookin', you ain't cookin'."

If you have a digital thermometer, you can check the meat and pull them off when they are about 170 - 175 F. Heat momentum will raise the meat an additional 5 degrees or so when they're off the grill (no need to rest chicken meat).

As the other poster said, don't put any sauce on until after the meat is cooked. You could brush on sauce and grill it over high heat for 30 seconds or so to warm the sauce, but that's it. The idea of letting the chicken meat absorb flavor from the BBQ sauce while cooking is a fallacy.

Good luck