Bisguier was born in a Jewish family in New York City and graduated from the Bronx High School of Science.

[1] He was taught chess at the age of 4 by his father Jesse (born Jechiel Max Bisgeier), a mathematician.

Throughout the 1940s, he was considered one of the United States' best players, with Larry Evans, George Kramer, and Walter Shipman.

[2] Army service interrupted his U.S. chess career during 1951 to 1953, but he managed to get leave to play in two European events.

[3] Bisguier represented the United States at five Chess Olympiads; his totals over 82 games are (+29−18=35), for 56.7 per cent.

His detailed results, from olimpbase.org: Following his U.S. title in 1954, Bisguier regularly returned to compete for the national championship, but was never able to repeat his success.

Bisguier continued to play regularly at the Metrowest Chess Club in Natick, MA until 2014.

[6] For many years, Bisguier was hired to play in towns throughout the U.S. to give exhibitions, and to popularize chess and the USCF.

Victor Niederhoffer, the hedge fund manager, took chess lessons from Bisguier as an adult.

Their second game was a draw, after which Fischer won 13 straight — perhaps the longest unbroken winning streak between grandmasters in history.