An Elephant Chest is an item that can be applied to tamed adult Elephants and Mammoths in order to give them their own inventory.
Two Elephant Chests can be applied to each Elephant or Mammoth. Woolly Mammoths can be given two extra Chest Sets.
Elephant Chests can only be applied once an Elephant Harness has been given to an Elephant or Mammoth. They can then be added by right-clicking on the Elephant. Once applied, a Key will appear in the player's inventory, which can be used to open the Chests (although in DEV v8.0.0, Keys will no longer appear and instead you can sneak and shift + right-click to open the Elephant/Mammoth's inventory).
Elephant Chests can be removed by right-clicking on an Elephant/Mammoth with Shears. Elephants will also drop Elephant Chests upon death, or when a Scroll of Freedom is used.