Jüri Randviir learned to play chess at age ten in Tartu, where he spent his school years.

[1] In 1955 he was second in the traditional National Tournament in Pärnu (won Paul Keres) and became a Soviet Master.

[2] Five times Jüri Randviir played for Estonia in Soviet Team Chess Championships (1953-1960).

As a freelance journalist worked with major Estonian newspapers and made radio and television programs about chess.

Since 1956 Jüri Randviir has given a large number of simultaneous exhibitions in which played approximately 2756 games (+2327 -131 =298).