Unquestionably the building of the coalition that defeated National Socialist Germany and led to the creation of the United Nations. The setting up of the UN was the single most ambitious political undertaking of the 20th Century, and although I personally think it has not been used to anything near its potential, I realize that is hardly possible given the idealogical differences among the nations. Still, the very idea of such a body and the fact that it functions at all is one of the outstanding political and diplomatic feats of history.
The creation of this coalition had to take place, at first, largely in secret. In the late 1930s cooperation among the intelligence agencies of Poland and Great Britain led to the discovery of the German coding/decoding machines nicknamed "Enigma", and the eventual intelligence coups of World War II. President Roosevelt, while the majority of Americans were determined to stay out of the war, realized that would be impossible in the end. He cooperated and led government agencies such as the FBI and military intelligence groups into secret cooperation with the British Security Coordination, led by a man code-named "Intrepid," one William Stephensen. All this led to the formation of intelligence networks and secret resistence armies across Europe, whose work was invaluable to the success of the Allies in the war. The work of those allies, most notably Britain and America, led to the creation of the UN. Only nations which formally declared war on the Axis powers were eligable for membership, resulting in a great many countries joining the coalition, although many of them (notably in Latin America) only joined in the last months of the war, when the end was all too clear. Still, this led to the only reasonably successful attempt at mass international cooperation in history. The fact that America could be brought to a point where a very large percentage of citizens ( perhaps even a majority) had come to believe that our entry into the war was inevitable even before Pearl Harbor, that such an international coalition could be built secretly before 1941 and openly after, and that so many diverse nations could be brought together and actually manage to more or less work together, together constitute the most significant political move of modern times, not just the 1940s.