Born at Misilmeri, Chinnici graduated in law at the University of Pelermo in 1947 and started working as a magistrate in 1952 in Trapani. In 1966 he moved to the prosecutors office in Palermo. In November 1979, he became Chief Prosecutor at the Palace of Justice in Palermo following the murder of his predecessor, Cesare Terranova, by the Mafia.
Chinnici created the Antimafia Pool, a group of investigating magistrates who closely worked together sharing information to diffuse responsibility and to prevent one person from becoming the sole institutional memory and solitary target. The famous Antimafia magistrates Giovanni Falcone and Paolo Borsellino were part of the Antimafia Pool as well as Giuseppe Di Lello and Leonardo Guarnotta.
On July 29, 1983 a car bomb explosion in Palermo killed Chinnici, two of his bodyguards, Mario Trapassi and Salvatore Bartolotta, and the concierge of his apartment block, Stefano Li Sacchi. The bomb was triggered by the notorious Mafia assassin Pino Greco and Pino acted under orders from his uncle Michele Greco. Michele Greco was subsequently sentenced to life imprisonment for ordering Chinnici's assassination.
Chinnici was replaced as Chief Prosecutor by Antonino Caponnetto.