August Eller participated in two Estonian schoolchildren chess championships (1925, 1926).

In 1944, August Eller tied for 1st-2nd with Johannes Türn in Viljandi (14th Estonian Chess Championship).

After World War II Eller imprisoned in Soviet prison camp but soon Red Army authorities realized he was freed from jail.

Eller participated in postwar Estonian Chess Championships in 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1958.

[3] In 1968 August Eller played for Estonia Sports Club Jõud in 6th Soviet Team Chess Cup in Riga, where his team finished at last place.