I never thought there was an official chair position either.
That was one of the reasons Luciano reshaped LCN into the its current structure was specifically to avoid a 'boss of bosses' mantle.

Now there have been defacto 'Chairs' IE Bonanno, Gambino, Chin etc and powerblocs within the commission itself, but imo, never an official chair title.

MORGAN: Why didn't you fight him at the park if you wanted to? I'm not goin' now, I'm eatin' my snack.
CHUCKIE: Morgan, Let's go.
MORGAN: I'm serious Chuckie, I ain't goin'.
WILL: So don't go.