Rabbi Chavel was born in Ciechanow, Poland in 1906, and moved to the United States in 1920.
He served as rabbi of Congregation Anshei Sfard of Louisville, Kentucky, from 1930 to 1945, and received his M.A.
He then spent a year as director of synagogue activities of the Union of Orthodox Jewish Congregations of America.
In 1979 he moved to Jerusalem and joined the Board of Directors of the publishers, Mossad HaRav Kook.
Most of Rabbi Chavel's books were devoted to critical editions, with annotation and commentary, of classical Jewish commentators on the Bible and Talmud.