Depending on age... I'd say no younger than 3 months. Other people do that, I wouldn't. If you're shipping to a cold area... I know Jerseys not too warm now... Try putting less holes and keep an official heat-pad inside, underneath the chameleon's container, with news paper ontop of the heat-pack. Make sure there is something like newspaper shreddings inside the box. I'd put a paper towel inside the container, and spray it once with warm water. Remember, not too many holes... you want the warmth to keep inside the box.
i took my chams to my parents house for the weekend awhile ago, all i did was throw their entire enclosure into the backseat of my car and strap them in. as long as the stuff in the enclosure cant move you should be fine, just drive easy. I think i stressed about the drive more than they did, their colors looked normal, on the way back they just slept the whole way. But as mentioned above, i wouldnt take them far if they are very young, my chams are juveniles and were healthy before the trip
Best way in my opinion to not stress your cham is to take a shoe box and put one of their vines in it with a rag/towel on the bottom with some strips of newspaper and 10 small holes. If you do not keep them in a dark place while traveling they will be stressed out. I travel 4 hours down and 4 hours back to my parents.