There has never been an official chairman. At times there has been one boss that is much more powerful than the others, but never a boss of bosses except in the media's imagination. The Gambinos and Genovese have always been pretty equal in numbers and strength, so neither side would allow the other to chair any meeting or be allowed to be a boss of them. Even when Carlo Gambino was the most powerful in the late 1960's til his death, I doubt that the Genovese would back down to him when it came to the labor rackets, construction, and gambling territory.

Then you had the two FBI agents who wrote the biography on Castellano calling him boss of bosses. Yet it was the Genovese who were behind the Angelo Bruno hit. It was the Genovese who had Castellano whack one of his own capos over a dispute.