Orchids can be absolutely grown in chameleon cages! They require different amounts of lighting. The most common, the phalaenopsis, or moth orchid, requires 'reading light'.
Go to lowes and find you one and give it a try. Key to a nice healthy orchid in the store is thick, firm feeling leaves that have strength to hold themselves up. If they look droopy, feel thin, or have 'ribs' on the leaves, avoid it. When you finally find one that looks healthy, buy it!
When you get home with it, my advice though is to get it out of the pot that it'll come in. It'll be planted in either soil, very fine bark like material, or sphagnum moss. If it's planted in moss, it's packed very tightly in it. Slowly work the moss under luke warm water and slowly work the moss away from the roots. Then check the roots, and with some scissors, snip off the brown mushy or black colored roots, and give it a good rinse. Look around the plant for any white fuzzies, black spots, or any bugs.
A happy way to keep your new orchid in a chameleon cage is mounted to to something, a piece of wood, check out
http://www.repotme.com/orchid-care/Mounted-Orchid-Care.html for ideas. I always use cheap panty hose from the dollar store to attach my orchids to something. Panty hose is softer for delicate roots, and as they grow, the panty hose won't 'cut' into roots like fishing line can. Why mounted? Because the constant misting/watering a in the cage can drown an orchids roots. Mounting them exposes the roots to the air, giving them the chance to dry out I between mistings.
Place your mounted orchid in the cage where it'll receive some lighting and some mistings and it should be a happy grower for you!
I hope this helps

I'm starting my orchid blogs up, so let me know what you all think.