Born in Brooklyn, New York in 1958, Zancocchio started working under Bonanno caporegime Dominick Napolitano in the early 1970s. After Napolitano's killing as a result of the Donnie Brasco scandal, Zancocchio worked for capo Anthony Graziano. During the 1980s, Zancocchio married Graziano's daughter, Lana (older sister of Mob Wives star Renee Graziano, and show creator Jennifer Graziano), making him brother-in-law to Bonanno mobsters Christian Ludwigsen and Hector Pagan Jr.