According to Joe Bonanno, in his autobiography, "A Man of Honor," the first chairman was Mangano. I believe him: It was typical of Charlie Luciano's businesslike attitude that he insist that someone else be the "chairman." Luciano arranged to have Salvatore Maranzano whacked because he pissed off all the Mafiosi when he declared himself "capo di tutti capi" and demanded a tribute from every Mafioso in NYC. Luciano naturally assumed the leadership of the Five Families after that, but he was smart enough not to make the same mistake Maranzano made. Mangano's "chairmanship" was a figurehead position--everyone knew that Luciano was the top Mob guy.
New Q: Who kidnapped Joe Bonanno?