January 1: Thailand Prime Minister Plaek Phibunsongkhram decrees January 1 as the official start of the Thai solar calendar new year (thus the previous year that began April 1 had only 9 months).
January 3: A decree in Germany outlaws the use of Blackletter Gothic typefaces in favour of Antiqua.
January 4: The short subject Elmer's Pet Rabbit is released, marking the second appearance of Bugs Bunny, and also the first to have his name on a title card.
January 5: At the Battle of Bardia in Libya, Australian and British troops defeat Italian forces, the first battle of the war in which an Australian Army formation takes part.
January 6: The keel of the USS Missouri is laid at the New York Navy Yard in Brooklyn.
January 10: The Lend-Lease Act is introduced into the United States Congress.
January 11: The British Royal Navy light cruiser HMS Southampton (83) is sunk off Malta.
January 13: All persons born in Puerto Rico since this day are declared U.S. citizens by birth, through U.S. federal law.
January 14: Commerce raiding German auxiliary cruiser Pinguin captures the Norwegian whaling fleet near Bouvet Island, effectively ending Southern Ocean whaling for the duration of the war.
January 15: John Vincent Atanasoff and Clifford Berry describe the workings of the Atanasoff-Berry Computer in print.
January 19: British troops attack Italian-held Eritrea.
January 20: Chief Justice Charles Evans Hughes swears in U.S. President Franklin D. Roosevelt for his third term.
January 22: Battle of Tobruk: Australian and British forces capture Tobruk from the Italians.
January 22: In Sweden, Victor Hasselblad registers the Hasselblad camera company.
January 23: Aviator Charles Lindbergh testifies before the U.S. Congress and recommends that the United States negotiate a neutrality pact with Adolf Hitler.
January 27: Attack on Pearl Harbor: Joseph Grew, the U.S. ambassador to Japan, reports to Washington a rumor overheard at a diplomatic reception concerning a planned surprise attack on Pearl Harbor, Hawaii.
January 30: Australians capture Derna, Libya, from the Italians. (source: Wikipedia)