DO NOT GIVE HIM ANY PAIN MEDS UNLESS PRESCRIBED BY A VET!!!!!
Tylenol is incredibly toxic to liver and has a very low margin of error. The difference between a therapeutic dose for humans and one that completely destroys the liver to the point of death or a liver transplant is really small. Tylenol for some animals, dogs for example, is deadly. Dusting a cricket with it? Just exactly how much drug would that be? Tylenol is a serious drug that kills a lot of people every year.
Other pain meds are fine for one species but deadly for another. Diclofenac, a non-steroidal anti inflammatory springs to mind. That drug is wiping out the vulture populations in India--the drug is given to livestock that end up dying and the vultures do their job and clean up the carcass but die from renal failure caused by the drug.
Each species of animal processes drugs and clears the drug out of their system at a different rate. For example, dogs take twice as long to process Aspirin than humans do. You can follow the directions and dose by weight correctly but if you don't increase the time between doses, you will have an overdose very quickly simply because the animal doesn't clear the drug at the same rate as humans do.
There are disadvantages with pain meds besides toxicity and their interference with the bone-healing process. Sometimes it is good to make sure the animal knows he is hurt so he will protect the hurt leg.
You are probably okay to just let it heal up on its own. I certainly wouldn't be handling him as he'll struggle to try to avoid the predator (you) and be more likely to hurt himself in the process of avoiding capture, regardless of how tame he is.
Some things to think about is why that leg is broken.
A natural defense strategy for chameleons is to drop out of the trees, sometimes from quite a height. I've read that sometimes females will do that to avoid a male. They don't usually break. I don't think a female would choose to avoid the unwanted advances of a male with a life-threatening escape strategy.
Does he have undiagnosed MBD? That would explain why he broke his leg from a small fall. There is, of course, also the possibility that someone handled him too roughly and either didn't realize it or is not coming clean.
Peti's fracture doesn't seem to involve joints, so when it heals, he should be fine.
When a bone heals, it dissolves itself at the edges of the fracture and forms a callus around the fracture, whether a complete fracture or just a crack. That callus is a natural cast. Your major concern with him is getting his calcium right so he will be able to heal. For that, you might want to take him to a vet for advice.
His fracture in practical terms is no different than the sad cases of MBD you see posted on this forum.
Good luck.
Well the only place in my area for a specialist veteran is fully booked until Friday. Over the phone it does not sound like there is much they can do except give him a pain injection, since he is so small they don't think they can splint it. Poor Petri is going to have to wait. I wonder if I can dust his crickets with some crushed Tylenol until his visit. Today I took him out for a better inspection and for a picture. I’m sure it’s broken, I can see and feel the snapped bone in his leg. The only thing I can do now is leave him alone and wait for his appointment. Here are some better pictures.