I use a box when traveling to my vet office. I line the bottom with a small towel incase they fall and add lots of branches to grab onto. Close the box so they don't escape, but you do want to have some air to pass through. Also, you want to make sure when you arrive home, get the enclosure ready and when you put them in, let them crawl out on their own into their new home and leave them be to acclimate and relax so you don't stress them. Works for Mojo with no problems.
Pillow cases are used for snakes and other reptiles for the breathability of the fabric and to keep it somewhat dark, but chams are a little more fragile and feel secure holding onto something so they need a hard enclosure.