Eskenazi was born April 23, 1960 in Queens, New York. He attended Bayside High School then studied psychology and American literature at Queens College. While at Queens College he was photo editor for the yearbook, assisted photographers on assignment and worked as a freelance photographer for the "Queens Tribune". After graduation he worked in darkrooms, obtained local photo assignments, continued as an assistant and interned at a photo agency in New York. At age 29, inspired by the fall of the Berlin Wall, he began to travel and make photographs. His first trips were to Romania (for its first democratic election) and to Germany, then Russia in 1991 just before the August coup that marked the end of the Soviet Union.