Named entities & named items in item frames make chests invisible.

If you name an item, put it into an item frame, and have the item frame on a chest, and then move your crosshairs or finger onto the item frame to display its name, you will notice the chest is invisible. Try moving around a lot. This may take a few tries!

EDIT by Zeb: This occurs with named entities, too. (Any entity name tag is affected by this.)