Hans Müller was an Austrian chess player, theoretician and author of books. In 1921, he played in Vienna; he tied for 9-10th, tied for 1st-2nd with Gruber, and took 6th. In 1922, he tied for 4-5th in Innsbruck. In 1923, he tied for 4-6th in Budapest. In 1924, he tied for 8-9th in Györ. In 1925, he tied for 1st-2nd in Debrecen. In 1925, he tied for 5-6th in Vienna. In 1926, he took 7th in Bardejov. The event was won by. The event was won by Karl Gilg and Borislav Kostić. In 1926, he tied for 5-6th in Hyères. In 1926, he tied for 8-9th in Vienna. The event was won by Spielmann. In 1927, he took 9th in Kecskemét. In 1927, he tied for 1st with Albert Becker in Vienna. In 1928, he took 8th in Vienna. In 1929/30, he took 3rd in Vienna. The event was won by Hans Kmoch and Spielmann. In 1931, he tied for 7-8th in Vienna. In 1932, he tied for 5-7th in Vienna. In 1932, Hans Müller won the European Correspondence Chess Championship ahead of Eduard Dyckhoff. In 1933, he won ahead of Erich Eliskases in Ebensee. In 1933, he tied for 1st with Grünfeld in Vienna. In 1934, he tied for 1st with Gilg in Klosterneuburg. In 1934, he took 3rd, behind Becker and Eliskases, in Linz. In 1934, he tied for 2nd-4th in Vienna. In 1935, he took 8th in Tatatovaros. In 1937/38, he tied for 3rd-5th in Vienna. Hans Müller played for Austria five times in the Chess Olympiads and once in unofficial at Munich 1936.
He won individual bronze medal at Folkestone 1933. After the Anschluss, he took 2nd, behind Eliskases, in Vienna in June 1939. Then, in July 1939, he tied for 10-13th in Bad Oeynhausen. The event was won by Eliskases. In May 1940, he took 3rd in Bad Elster. In November 1940, he tied for 5-8th in Kraków/Krynica/Warsaw. The event was won by. The event was won by Paul Felix Schmidt and Klaus Junge. In July 1942, he tied for 2nd-3rd, behind Ludwig Rellstab, in Bad Oeynhausen. In September 1942, he tied for 3rd-5th in Munich. In August 1943, he took 4th in Vienna. The event was won by Josef Lokvenc. In 1943, he took 8th in Vienna. In December 1943, he took 2nd, behind Grünfeld, in Vienna. In 1944, he won in Posen. After World War II, Müller played in several Austrian championships since 1947 till 1960. He took 6th in Vienna in 1947. The event was won by Szabó. In 1949, he took 14th in Venice. In 1949, he tied for 8-9th in Vienna. The event was won by Jan Foltys and Puc. In 1949/50, he took 5th in Lucerne. In 1950, he took 14th in Venice. In 1950, he tied for 8-9th in Vienna. In 1951, he tied for 8-9th in Vienna. The event was won by Moshe Czerniak. In 1957, he tied for 7-8th in San Benedetto del Tronto. Hans Müller played for Austria in friendly matches against Czechoslovakia, Italy and the Soviet Union. He was awarded the IM title in 1950.