Always and always close the clasp on your chain. Whether you hang your necklaces or store them in a jewelry bag or a box, it is very important that you close the clasp before you store them. That should hopefully save you some trouble.
This method works most of the time. Moreover, there is something else I learned recently on how to store necklaces when you travel: Straw Method
Simply thread your necklace through a straw and close the clasp.
... Hope these small tricks will save you some time.