The board and the CEO have very different roles. The chairman is one of the board members who is elected by other members.
The CEO has the responsibility of running the day-to-day operations of the company.
The board’s responsibility is to provide overall direction; set vision & goals; oversee governance & integrity and take major strategy decisions [e.g. change of the business model], etc.
In addition to the founders and representatives of investors, it is prudent to have a few independent directors on the board. These are often senior folks with a lot more experience than the operating team and can be very very useful as a sounding board while taking tough decisions as well as for the motivation that would be required when the business is going through rough times.
In many ways a board member can provide ‘adult supervision’ to young founders and CEOs.
The CEO executes the vision and the direction set by the board.