The quietest place on the planet is in Minneapolis, MN at Orfield Laboratories.  That's where they have built an anechoic chamber that is 99.99% sound proof.

The silence is so maddening, that the record for sitting in the silence in the dark is 45 minutes.  Volunteers begin to hallucinate, go crazy over the sound of their own bodily functions, and basically just lose it.  Pretty weird!

Other interesting facts about a sound proof room:

If you stand in the dark too long, you'll lose your balance since you use hearing for balance.

The chamber is used by many manufacturers to test how loud their product is.

The chamber holds the Guiness Book Of Record for quietest place.

Read more about it at the dailymail.