Looks to me, not 100% sure...
that what happened was he is/was getting burned while basking and the screen (if the bulb is too hot/close enough) can actually get hot enough to cut them like that. i've heard horror stories of it happening to veiled chams quite often. i'd suggest scheduling a vet appointment, just to get it checked out and get some medication to stay clear of infections. I can't see all of him so i don't know if his back is burned or not. but do his hands look okay? if he was climbing upside down is crest across the bottom or his hands may also be a little "fried".
This is easily avoidable if it's the case and treatable but it will scar and as for the loose part of the "skin" don't touch it try to keep him warm and get him to drink for right now (never try to force a cham to drink... but you know what i mean, offer him some water. he does look a little dehydrated.), if an exotic vet is near you i'd take him right away personally. It's getting kinda late where i am, don't know about you.
Reevaluate your bulbs and let us know some information on the enclosure and bulbs and all that, pics are nice for enclosures.
not trying to come off as abroken record... but call a vet.