Hacham Abraham Chen was born to Esther and Shimon in 1911 in Jerusalem's Old City. As a young man, he moved from the Old City with his parents to the Nachalat Shiv'a neighborhood. He was educated at the Doresh Zion Talmud Torah and then studied towards his teacher's certification at the Lipfshitz Teacher's College. He taught during his entire life, first as an educator at the Beit Aharon school for 24 years, then as a school principal in several new schools established in the city of Beit Shemesh, and at the Yeshurun School in Jerusalem's Kiryat HaYovel neighborhood, initially a small school that subsequently grew into a large, successful and renowned school. During Israel's War of Independence (1948) he devoted himself to the special educational missions dictated by the difficult circumstances, for which he received an honorary award from the National Teachers Union.
Abraham Cohen was a generous and charitable person; he worked at the Eliyahu School, a special school for employed youth, during many years. These youths were children of new immigrants who had to work to contribute to their families' income. Abraham Chen gathered them and provided them with learning skills, while during their remaining time they worked to help out their families.
Even after retiring, he continued to help others through charitable acts, volunteering at Yad Sarah, and taking on the role of beadle in the Kiryat Moshe Institute for the Blind in Jerusalem. He would give sermons at this synagogue on Sabbaths and festivals, and strove to integrate the institution's blind members with the neighborhood residents.
In 1995, he published Avnei Chen, where his thought is presented in the order of the weekly Torah reading portions.
Avraham Chen passed away on 3 Tishrei 5675 (2005), on the Fast of Gedalya, at the age of 94 and was buried in Jerusalem. Following his son's request, in keeping with his father's request during his lifetime, the title Hacham was not used before his name.