How can I make a chest Unbreakable in Minecraft?

You can use command blocks to set an area to adventure mode, this could be used so that the room with the chest in can't have blocks broken.

This command will set adventure mode for anyone within a radious of 20 blocks. Just have this activated by a pressure plate or two as they enter the room or leave it.

/gamemode 2 @a[m=0,r=20] (r=20 will set the area radius to 20 blocks)

This will set the gamemode to normal for anyone outside of 20 blocks

/gamemode 0 @a[m=2,rm=20] (rm=20 will set the mode for anyone that is more than 20 blocks away.

Just change the radius and the position of the command blocks depending on your situation. Source

Instead of unlocking the chest that has the loot in it, make the key unlock a trapped chest that sends a redstone signal to a secret door, with the actual loot in another chest behind the door.