The way you can keep your Chillow free from mildew is to keep it from touching any surface that does not absorb water when it is not in use. This is due to the Chillows temperature is now being higher than the surrounding air temperature. This will cause condensation to occur until it releases it's heat back into the air. Moisture and heat will naturally cause mildew if there is any bacteria present. We humans are covered in the stuff and will transfer it to the surface of the Chillow and presto.
Do not leave it folded over on it's self and store it flat on a clean dish towel when not in use.