In 1966, Conrad was involved in a controversial attempt to climb Vinson Massif. Vinson is the highest mountain in Antarctica, located about from the South Pole. That year, a team of climbers were sponsored to climb the mountain by the American Alpine Club and the National Geographic Society, and supported in the field by the U.S. Navy and the National Science Foundation Office of Antarctic Programs. At the same time, an unauthorized attempt was announced by Woodrow Wilson Sayre, who was planning to fly in a Piper Apache piloted by Conrad with four companions into the Sentinel Range to climb the Vinson Massif. Sayre had a reputation for problematic trips as a result of his unauthorized, unsuccessful, and nearly fatal attempt to climb Mount Everest from the north in 1962. His unauthorized incursion into Tibet led China to file an official protest with the U.S. State Department. However, the attempt did not materialize. Conrad had difficulties with his plane, and according to press reports at the time, he and Sayre were still in Buenos Aires on the day the first four members of authorized team reached Vinson's summit.