Nope, it is not about color pigments. It is about pigments and crystals. Within the skin the chameleons have tiny cells full with nanometer sized crystals. When the position of the crystals in those cells change, the color it reflects changes too. This process is called structural coloration and the colors created through this process are called iridescent colors.
Look, ma, the peacock does the same thing: iridescent colors via the structural coloration process.