Just Imagine.
J F Kennedy, address before the 18th General Assembly of the United Nations (20 September 1963)
Finally, in a field where the United States and the Soviet Union have a special capacity - in the field of space - there is room for new cooperation, for further joint efforts in the regulation and exploration of space. I include among these possibilities a joint expedition to the moon. Space offers no problems of sovereignty; by resolution of this Assembly, the members of the United Nations have foresworn any claim to territorial rights in outer space or on celestial bodies, and declared that international law and the United Nations Charter will apply. Why, therefore, should man's first flight to the moon be a matter of national competition?
You gotta wonder what the hell would have happened.