How do you get minecart hoppers to put items in chests?
Solution 1:
You can't directly place a rail on a chest but you can place a rail on a hopper. Just make sure the hopper is not powered or it will not work.
Below I've included an Image on how to set it up
By the way, the rails don't have to be powered, but you can risk de-activating it using an activator rail.