Steve is right on. I cook on gas all the time. Preheat the grill for at least 15 minutes, and then treat it like an oven. I'm not sure which Weber you have, but I know the configuration. Once the Grill has warmed up, check the thermometer in the lid. They are not exactly accurate, but are a good approximation. If there are 2 burners, turn one off and leave the other around the middle setting. If there are 3 burners, I tend to turn off 2 of them, and leave the remaining one at medium, or turn the front and back ones to low and the middle off and kinda move the chicken towards the middle, so it is more indirect heat. At those settings the grill should hover around 350-400 degrees. It becomes just like roasting in your oven. Keep the chicken from directly over the burners to minimize the amount of flare-ups.
If you are looking for a little more smoke flavor, which you don't typically get on gas grills, create a foil packet with some soaked wood chips in it. Poke a few holes and throw that below the grates a few minutes before putting the chicken on to give it a chance to ignite and smoke. You can also throw chunks under the grates near the burners and get them to ignite, but it does not always work as well.
Once the chicken is nearing done, if the skin is not crisped to your desired level, crank the heat up like you would in the oven. Most Webers can easily get to 600+ degrees with the burners cranked, which will crisp the skin quickly.