Rabbi Eliyahu ben Moshe Chaim was born in Baghdad in 1807 (5567). He was the youngest son of Rabbi Moshe Chaim, rabbi and av beit din of Baghdad and leader of the whole community. He learned Torah from his father and became renowned as a great master of both the revealed Torah and Kabbalah.

When his father died in 1836 he succeeded him as the community's preacher. He spoke every Shabbat on the weekly portion in his synagogue, and on the three great Shabbatot of the year, Shabbat Shuva, Shabbat Zachor and Shabbat HaGadol, all the Jews of Baghdad gathered in the great synagogue to hear him, while the city's other preachers refrained from speaking.

A kabbalist, halachic authority and successful merchant, he devoted much of his earnings to supporting scholars and the poor. Known for his integrity, he was entrusted with Baghdad's fund for the kollelim of Jerusalem, and made up the sum from his own pocket when donations fell short. He also helped Rabbi Avraham Antebi, rabbi of Aleppo, to finance the printing of his books.

He was the father of Rabbi Yosef Chaim, the Ben Ish Chai, whose greatness he recognised early. He passed away on 7 Elul 5619 (1859) at the age of 52; Jews and non-Jewish dignitaries of Baghdad attended his funeral. At the end of the seven days of mourning his son gave his first public sermon and took up the leadership of the community, which he guided for fifty years.