In January 1945, Mao Tse-tung  sent a message to U.S. President Roosevelt asking to visit the U.S. and discuss future relationships with China. The message got blocked by a U.S. diplomat in China, and Roosevelt apparently did not receive it. But its existence is not disputed. Mao’s request was even referenced by the same diplomat in his telegram to Roosevelt some days later.
By 1945, Mao’s armed forces had gained the upper hand in the fight against the Japanese in China, outdoing the Koumintang troops run by Chiang Kai-shek, despite the latter getting much more military support from the Americans. The U.S. was basically backing both sides in China at this point. It knew that Chiang was a self-aggrandising crook (his nickname among American diplomats was ‘Cash My Check’). Some U.S. diplomats were also open to the ‘communists’, seeing them only as focusing on agrarian reform and economic development, and also recognising their military prowess. Remember too that this was a time for the Americans when rabid anti-communism had not yet fully taken hold, and it was in any case focused on the Soviet Union.
According to an important article by Barbara Tuchman, the previously mentioned diplomat, Patrick Hurley, was following the basic line of American policy. This was to get unity of the two Chinese forces, but under the control of the Kuomintang. The growing relative strength of Mao’s side was underestimated, and U.S. officials believed that a ‘democratic’–and pliable–China was there for the taking after the defeat of Japan. They did not anticipate the anger with which the apparent U.S. rejection of the request from Mao would be received.
Yenan Government wants [to] dispatch to America an unofficial rpt unofficial group to interpret and explain to American civilians and officials interested the present situation and problems of China. Next is strictly off record suggestion by same: Mao and Chou will be immediately available either singly or together for exploratory conference at Washington should President Roosevelt express desire to receive them at White House as leaders of a primary Chinese party.
One can speculate on what might have happened if Mao and Chou En-lai had made the trip, which would have been Mao’s first trip outside China. Tuchman recognises that many other domestic U.S. and world political events made it very unlikely, even if the original telegram had got through, and even if Roosevelt had lived longer. But she notes that there might have possibly been a different future course of events, including for Korea just a few years later.
There is a lot of mythology about the history of Chinese communism. China was backed into a corner by imperialism, war and the threat of further intervention. But Mao would have been happy to come to some kind of deal with the U.S.–not the colonial British and French–to get support for economic development.
The images below are from pages 10 and 12 of a long telegram from Hurley to Roosevelt on 13 January 1945.
 Here I shall refer to the old anglicised spellings of the Chinese names, given the telegrams noted below from 1945.
 ‘If Mao Had Come to Washington in 1945: An Essay in Alternatives’, Foreign Affairs, October 1972. Much of the information here is taken from this article, which also gave good references allowing a search of the U.S. official archives. I could find no online copy of the original message from Mao to Roosevelt that was relayed via U.S. military observers in Yenan to the U.S. office in Chungking, China, but note its message in the main text, using Tuchman’s article. I did find a copy of Ambassador Hurley’s later telegram to Roosevelt in January 1945 that confirmed such a request had been made, shown in the two images above. An amusing biographical profile of the ‘erratic’ Hurley is available on Wikipedia.