I use RO water for both my misting and rain system (having just recently changed from tap water because I dont like the build up of mineral deposits on the glass), my chameleon drinks from this. My only issue with RO water and im not sure if its even an issue... is it's "pure" water, there are no minerals or salts containied in the water (litterally just good old H20). I dont know where you live in the world, but most tap water is ok. If you are unsure take a sample to a tropical fish store and get it tested for chemicals and PH etc. The only issue with tap water is it often contains minerals which cause things like a build up of limescale which leaves a horrible stain on the glass if you use a glass enclosure and is a pain to clean.
Alternatively you can buy something to stick on top of a saucepan and boil the water yourself.. the steam evaporates and runs down the tube leaving all the minerals in the pan... I have seen one of these before... no idea where to get them though!? That's the only thing I can think of... otherwise you will have to fork out for it... these are one of the things that aren't cheap and you dont want to buy a cheap one becuase it will most likely do 1/2 the job.