Whispering Keys are a unique item in Diablo IV that can be used to unlock Silent Chests found on the world map. The game does not outright tell you how to obtain them, but getting your hands on one of these highly valuable keys is a lot easier than you might imagine. In order to obtain Whispering Keys in Diablo IV, so you can unlock Silent Chests to obtain rare items and loot, you need to speak to the Purveyor of Curiosities Lizveth in Kyovashad.
You can see where Lizveth is located in Kyovashad below.
Lizveth will sell you Whispering Keys for 20 Obols. Obols can be obtained by doing World Events on the map. These events populate the map at random or can be triggered by talking to various NPCs you find as you roam Sanctuary. An easy way to spot if a World Event is happening nearby is to look at your mini map at the upper right-hand side of your screen. If you see a very faint ring of red, that means a World Event is nearby.
The better you do at a World Event, the more Obols you will obtain. Doing World Events with a group, or at least one other person, will almost guarantee completion of the event even on Veteran Difficulty. That said, if you fine-tune your build enough and have the right gear, then you will be more than capable of tackling these events on your own.