In 1930 Moshe Czerniak took ninth at Warsaw in an event won by Paulino Frydman.

In April 1935, he tied for 7th–8th in Tel Aviv (the 2nd Maccabiah Games, Abram Blass won).

In April 1939, he played in the First Lasker Chess Club Championship in Tel Aviv.

[3] In September 1939, when World War II broke out, Czerniak, along with many other participants in the 8th Chess Olympiad, decided to stay in Argentina.

[4] Immediately after the 8th Olympiad, in October 1939, he tied for 3rd–4th with Gideon Ståhlberg, behind Miguel Najdorf and Paul Keres in the Buenos Aires 1939 chess tournament (Circulo).

In 1941, he took 2nd, behind Paulino Frydman in Buenos Aires, and tied for 6th–8th in the Mar del Plata 1941 chess tournament.

In 1949, he took 4th in Mar del Plata, and tied for 3rd–4th in Argentine championships (Torneo Mayor).

For more than thirty years he was the chess editor of the Israeli daily Haaretz.