Taking your chamelon to the vet doesn't have to be a "big" problem - for you or the vet's office staff.
Transporting them in large cages is usually out of the question (too bulky for most cars; plants may fall over; too bulky to carry; etc.)
We use appropriately sized "critter keepers"
There are lots of sizes, and you only want to be sure the animal can turn around inside it - not be stuffed in. These plastic boxes have ventilation and many come with handles for carrying.
We place a clean, moist paper towel in the bottom, place the cham inside (make sure not to pinch the tail or a toe), and carry along a lightweight towel to drape over the carrier. While sitting in the vet's office, you can ease the stress by keeping him covered. Then once inside the exam room, you can use the towel to put over the stainless table for you cham to climb on. This is handier than you may imagine!
Good luck with your visits,
Morgana - Reptayls, Ltd.