It's in the Pacific Ocean, in the so called Marianas Trench, almost 11 km deep (6,8 miles deep or, in feet, 36 thousands feet deep). Let me copy this verbatim from Wikipedia entry on "Mariana Trench":
The Mariana Trench or Marianas Trench is the deepest part of the world's oceans. It is located in the western Pacific Ocean, to the east of the Mariana Islands. The trench is about 2,550 kilometres (1,580 mi) long but has a mean width of only 69 kilometres (43 mi). It reaches a maximum-known depth of about 10.91 kilometres (6.78 mi) (35,800 ft) at the Challenger Deep, a small slot-shaped valley in its floor, at its southern end, although some unrepeated measurements place the deepest portion at 11.03 kilometres (6.85 mi). (from Wikipedia's entry on "Mariana Trench").
"The Challenger Deep is the deepest known point in the Earth's sea floor hydrosphere, with a depth of 10,898 m (35,755 ft) to 10,916 m (35,814 ft) by direct measurement from submersibles, and slightly more by sonar bathymetry." ---------- http://en.wikipedia.org/wiki/Challenger_Deep