Storing wouldn't have anything to do with a chlorine smell.
Like others, I would start by suspecting your RODI system. Once your carbon stage has expired, chlorine will degrade your membrane, quickly exhaust your DI and easily make it to your RO vat.
If your water system uses chloramines, then even partly degraded filters can allow nasties through, including ammonia.
If not your filter, then I would suspect the reservoir wasn't pre-cleaned sufficiently.
If not that, then I would hope someone accidentally added bleach to your water and that it wasn't malicious.
-Matt