Kalichstein was born in Tel Aviv, then part of British-administered Mandatory Palestine, on January 15, 1946. After the new state of Israel was established, Kalichstein studied piano there with Joshua Shor. His playing caught the attention of pianist Claudio Arrau, who recommended Kalichstein for admission to the Juilliard School in New York. Kalichstein studied there with Edward Steuermann and Ilona Kabos. An early breakthrough for Kalichstein was a win at the Young Concert Artists competition in 1967. The following year, Kalichstein appeared as a soloist with the New York Philharmonic Orchestra under conductor Leonard Bernstein, playing Beethoven's Piano Concerto No. 4 in G major, Op. 58. The concert was televised nationally in the U.S. Kalichstein completed a master's degree at Juilliard in 1969, and in 1970, he won the prestigious Leventritt Prize, impressing a jury that included conductors George Szell and William Steinberg and pianist Rudolf Serkin. The prize gave Kalichstein the opportunity to perform with several leading U.S. orchestras, and he gave concerts with the New York Philharmonic and Cleveland Orchestra under Szell's baton. In 1970, he appeared with the London Philharmonic Orchestra, with André Previn conducting.
Kalichstein went on to an international concert career, appearing with top orchestras under such conductors as Daniel Barenboim, Pierre Boulez, and Christoph von Dohnányi. His chamber music career began in 1977, when he, pianist Jaime Laredo, and cellist Sharon Robinson were engaged to perform at the inauguration of U.S. President Jimmy Carter. The three musicians felt a rapport, organized further concerts, and formally established themselves as the Kalichstein-Laredo-Robinson Trio in 1981. In 1983, Kalichstein joined the faculty at Juilliard, remaining associated with the school until his death. Kalichstein continued to perform as a soloist, and in 1987, he recorded the two piano concertos of Mendelssohn with the Scottish Chamber Orchestra (with Laredo conducting) for the Nimbus label. He made several more solo recordings for Vanguard (music by Prokofiev and Bartók) and Koch International (Robert Schumann, Clara Schumann, and Brahms), as well as some 20 albums with the Kalichstein-Laredo-Robinson Trio, the last of them in 2014. Kalichstein died in Maplewood, New Jersey, on March 31, 2022. ~ James Manheim, Rovi