January 1 – The Federation of Rhodesia and Nyasaland is dissolved.

January 5 – In the first meeting between leaders of the Roman Catholic and Orthodox churches since the fifteenth century, Pope Paul VI and Patriarch Athenagoras I of Constantinople meet in Jerusalem.

January 6 – A British firm, the Leyland Motor Corp., announces the sale of 450 buses to the Cuban government, challenging the United States blockade of Cuba.

January 8 - U.S. President Lyndon B. Johnson's War on Poverty

January 9 – Martyrs' Day: Armed clashes between United States troops and Panamanian civilians in the Panama Canal Zone precipitate a major international crisis, resulting in the deaths of 21 Panamanians and 4 U.S. soldiers.

January 11 – United States Surgeon General Luther Terry reports that smoking may be hazardous to one's health (the first such statement from the U.S. government).

January 22 – Kenneth Kaunda is inaugurated as the first Prime Minister of Northern Rhodesia.

January 28 – A U.S. Air Force jet training aircraft that strays into East Germany is shot down by Soviet fighters near Erfurt; all three crewmen are killed.

January 29 – February 9 – The 1964 Winter Olympics are held in Innsbruck, Austria.

January 29 - The Soviet Union launches two scientific satellites, Elektron I and II, from a single rocket. - Ranger 6 is launched by the US space agency NASA, on a mission to carry television cameras and crash-land on the Moon.

January 30 – General Nguyễn Khánh leads a bloodless military coup d'état, replacing Dương Văn Minh as Prime Minister of South Vietnam. (source: Wikipedia)