bisguier was born in new york city and graduated from the bronx high school of science. he was taught chess at the age of 4 by his father, a mathematician. in 1944, aged 15, he was third at the bronx empire chess club. in 1946, aged 17, he came fifth in the u.s. open at pittsburgh, followed by seventh place in 1948. later that year, he took the u.s. junior championship and was invited to the new york city 1948–49 international tournament. throughout the 1940s, he was considered one of america's four most "dangerous" players, along with larry evans, george kramer, and walter shipman. as he gained in strength, bisguier was coached by master alexander kevitz.