Chitman was born in Giv'at Shmuel and lived all his life in Ramat Gan. His parents, Holocaust survivors, followed a traditionalist Jewish lifestyle; his father served as a cantor. He and his siblings attended secular schools. At home they listened to the Beatles, the Rolling Stones, Enrico Macias and opera along with liturgical and religious songs. When Chitman was 11, his parents gave him his first guitar, which he taught himself to play. When he turned 17, he received a piano from his grandmother. From 1971 to 1973, he served in the Israeli Central Command military entertainment troupe, along with Shem Tov Levy, Shlomo Bar-Aba, Dorit Reuveni and others.
His career began in 1976, when he composed a popular melody for Adon Olam. He became a popular Israeli artist during the 1980s and 1990s. He composed and wrote over 650 songs. His most famous songs include Noladati Lashalom (I Was Born for Peace), Ratziti Sheteda (I Wanted You to Know), Todah (Thank you), Mi yada' sh'kach yihiye (Who Knew It Would Be Like This) and Kan (Here), which reached third place during the 1991 Eurovision Song Contest. Chitman also appeared on the 1980s children's programmes Parpar Nechmad and Hopa Hei and Shirim K'tanim.