The air at the top of Mount Everest is thin. Very thin. So thin that most people have to breathe pure oxygen when they climb the peak. Those that don't risk hallucinating or passing out. In order for helicopters to operate correctly, they need some air resistance for their propellor. This is often why helicopters are not able to fly high into the mountains.
However, one helicopter did fly and land on top of the highest peak in the world. On May 14, 2005, French pilot, Didier Delsalle became the first pilot to land a helicopter on Mount Everest. By landing at 29,035 feet up, Delsalle broke the highest elevation helicopter landing record. Along with the very thin air, Delsalle had to land the craft in 75 mph winds and on top of snow that could have been very unstable.
He actually made the landing twice to make sure that it was repeatable too. To qualify as a landing, the helicopter had to be down for at least 2 minutes. The first time, he touched down for 3 minutes and 50 seconds and the second day, he touched down for 4 minutes. As one climber noted, Delsalle's record gives hope for helicopter rescues on the dangerous peak in the future.