A Chairman is the presiding official of an assembly, meeting, committee or party. In a corporation, the Chairman of the board of directors can also hold the position of Chief Executive Officer.
In China, Mao Zedong was Chairman of the Communist Party from 1935 to 1976 - and Chairman of its state, the People's Republic, from 1949 to 1959. (ENT: "Storm Front, Part II")
On Ekos, Eneg was the Chairman of the Nazi Party during the 2268 crisis in state leadership. (TOS: "Patterns of Force")
The Cardassian Detapa Council was lead by a chairman. (DS9: "Return to Grace") Cardassian Doctor Crell Moset was the Chairman of Exobiology at the University of Culat in 2371. (VOY: "Nothing Human")
Pascal Fullerton was the chairman of the New Essentialists in the 2370s. (DS9: "Let He Who Is Without Sin...")
Quark and Rom were both chairmen of the short-lived Ferengi Benevolent Association in 2371. (DS9: "Prophet Motive")
In 2374, Nilva was Chairman of the Slug-o-Cola beverage company. (DS9: "Profit and Lace")
In 2375, Koval was the Chairman of the Romulan Tal Shiar. Senator Vreenak was Vice-Chairman in 2374. (DS9: "Inter Arma Enim Silent Leges", "In the Pale Moonlight")