Rabbi Avraham HaKohen of Kalisk was born in 1741 in the townlet of Kalisk (Kalyshki, today in Belarus, east of Vitebsk), the son of Rabbi Alexander. As a young man he was known as a prodigy and, according to en.wikipedia, studied in his youth with the Vilna Gaon. He then drew close to Rabbi Dov Ber, the Maggid of Mezritch, and became one of his most fervent disciples. He married Ruchama, the Maggid's sister and the widow of Rabbi Noach Altschuler.

Many chassidim gathered around him, devoted to his path of great enthusiasm and intense devekut. The unusual conduct of his followers aroused fierce opposition; Rabbi Shneur Zalman of Liadi later wrote that it had been among the causes of the bans issued against the chassidim in Lithuania, and after the Maggid's passing in 1772 much of the opposition to chassidism was directed at him and his disciples.

In 5537 (1777) he joined the convoy of chassidim who went up to Eretz Yisrael under the leadership of his companion and teacher Rabbi Menachem Mendel of Vitebsk, serving as his right hand; his signature appears beside Rabbi Menachem Mendel's on most of the letters sent to the Diaspora. He stayed in Safed after the chassidim were forced to leave the city for Tiberias in 5541 (1781), joining them only two years later. In Tiberias he founded his own beit midrash next to that of Rabbi Menachem Mendel.

When Rabbi Menachem Mendel of Vitebsk passed away in 5548 (1788), he became head of the chassidic community in Eretz Yisrael, which he led for twenty-two years, and was among the founders of the fund for the Holy Land. His many letters, urging the chassidim abroad to support their brethren and offering them spiritual guidance, give a clear picture of chassidic life in Tiberias. After the publication of the Tanya a sharp dispute arose between him and Rabbi Shneur Zalman of Liadi: he held that the guidance of the chassidic public should rest on faith in the sages and simple fear of Heaven, with the study of the Torah's secrets reserved for an elite. Rabbi Nachman of Breslov tried to make peace between the sides during his visit to Eretz Yisrael in 5559 (1799).

His tract Chessed LeAvraham was printed at the end of the book of the same name by Rabbi Avraham HaMalach, and his letters were published in many collections. He passed away on 4 Shevat 5570 (January 9, 1810) and is buried in the old cemetery of Tiberias. His tombstone reads: "Here lies our master, the great and holy Rav Avraham, son of Rabbi Alexander, Kohen to the Most High God."