Born in Innsbruck, Austro-Hungarian Empire, he learned chess at the age of 12 and at the age of 13 was refused membership in the 'lnnsbrucker Schachgesellschaft' because of his youth. At the age of 14, in 1927, Eliskases played his first tournament in the Schlechter Chess Club and shared first prize. One year later, at the age of 15, he took part in the Tyrolean Championship and scored a convincing victory (with 7 points out of 8 games). This won him the right to participate in the tournament for the Austrian Championship in 1929 and the result was he shared first place with Esra Glass and became the youngest player ever to win the Austrian championship.
In 1931/32 while in college, he joined the Hietzing Chess Club and was challenged to an informal match by Ernst Grünfeld, who won the match by a narrow margin. In college he studied business but after his results at the Olympiads of 1930, 1933 and 1935 he devoted his time to chess. He won the German national championship at Bad Oeynhausen in 1938 and 1939 and played under the German flag at the 1939 Buenos Aires Olympiad, during which WW2 began
Among his best results were outright or ties for first place at Budapest 1934 (the Hungarian Championship), Linz 1934, Zurich 1935, Milan 1937, Noordwijk 1938 (his greatest success, ahead of Euwe and Keres), Krefeld 1938, Bad Harzburg 1939, Bad Elster 1939, Vienna 1939, São Paulo 1941, São Paulo 1947, Mar del Plata 1948, Punta del Este 1951 and Córdoba 1959. His victory in Noordwijk began a streak of eight consecutive tournaments in which he was undefeated. He won matches against Efim Bogoljubov (1939) and Rudolf Spielmann (three times in 1932, 1936 and 1937).
Towards the end of the 1930s, along with Keres and Capablanca, Eliskases was regarded as a potential contender for a World Championship Match with. Indeed, Alekhine was in favor of a match with Eliskases, who had been Alekhine’s second during his second match against Euwe in 1937.
After Austria's incorporation into the Third Reich, Eliskases seems to have come to the conclusion that his style of play was too cautious and he began take a more aggressive approach and he scored his greatest successes.
It was after his success in Noordwijk in 1938 (first prize +6 =3 -0) that he won six strong tournaments: the German Championship at Bad Oeynhausen in 1938, Krefeld 1938, Bad Oeynhausen 1939 (the German Championship again), Bad Elster 1939, Bad Harzburg 1939 and the Vienna 'Wertungsturnier' of 1939. In the same year, he played a match against Efim Bogoljubow, winning with a score of +6 =11 -3.
After these successes he was supported by the 'Grossdeutscher Schachbund' (GSB). Eliskases was flattered to play the part of the 'upright German', who it was felt was going to win recognition for the 'German style of fighting chess' and he began, for the rest of his life, to dedicate himself to the purity of the German language.
Eliskases was described as a polite and pleasant person and the GSB had high hopes for him. Alekhine, in his anti-Semitic tract 'Jewish and Aryan Chess' (1941), referred to Eliskases as his most best successor writing, “…it would be of much greater service to the world chess community if, for example, Keres or Eliskases became the title holder. And if in fact the one or, the other should prove to be a better player, I would acknowledge this quite ungrudgingly. But who is the better of the two? To be sure, Keres has a truly attractive ´Morphy style´, Eliskases’ chess is much comprehensive, evoking the notion of a truly universal style of chess. Can it really be considered mere chance that Eliskases beat the Estonian grandmaster not only at Semmering in 1937 but also in Buenos Aires?”
During the Olympiad of 1939 in Buenos Aires, where two Austrians (Eliskases on board 1 and Albert Becker) played in the German team, he along with many other players decided to stay in Argentina rather than return home. Brazilian authorities threatened to intern and expel him but some Brazilian players helped him avoid expulsion by hiring him as a chess teacher. Eventually he became a naturalized Argentine citizen and represented Argentina at the Olympiads of 1952, 1958, 1960 and 1964.
Eliskases was also a strong correspondence player, scoring over 75 percent during his most active period. He started playing postal chess in 1928 and here took third place in the Dyckhoff Memorial Tournament of 1932, an unofficial world CC championship for postal chess.
He was considered an expert in the endgame and Dutch GM Hans Ree observed that Eliskases was one of only four players (Keres, Reshevsky, and Euwe being the others) to beat both Capablanca and Fischer
FIDE awarded Eliskases the title of International Master in 1950 and Grandmaster in 1952. He was not named GM in the list of original titles awarded in1950, but in1952. It was also in 1952 that Bogoljubow was awarded the title. The reason for the late awarding of the title to Bogoljubow was because his political activities for the Nazi’s had been under scrutiny. As for Eliskases, he had never been under scrutiny and no accusations had ever been made against him, so the reason for the ‘late’ award is not known.
After the war Eliskases, who had become an Argentine citizen, resumed his career but he was no longer among the world’s elite players. He played in many South American tournaments during the 1950’s to 1970’s with only fair results.
Rossetto, Pilnik, Laurens, Maderna, Eliskases, Najdorf and Bolbochan, 1952
In 1976, he retumed to his native Austria with his wife and son, intending to settle there, but after 6 months they returned to Argentina. The last years of his life were spent in Cordoba where he suffered from illness and depression.