The quietest place on earth is actually at Microsoft, and it has the means to prove it. Here's a video about measuring the anechoic chamber at the company's Audio Lab to enter into the Guinness Book of World Records.
The chamber measures an astounding -20.6 dBa, which is essentially just the sound of air molecules knocking into one another.
Also check out this pretty cool virtual look at the Microsoft Audio Lab.
Thanks to my buddy Jesse Jaye for the heads up.