My all time favorite post on this topic
http://avc.com/2010/08/what-a-ceo-does/
A CEO does only three things.
1) Sets the overall vision and strategy of the company and communicates it to all stakeholders.
2) Recruits, hires, and retains the very best talent for the company.
3) Makes sure there is always enough cash in the bank.
great CEOs can and often will do a lot more than these three things. And that is OK.
But if you cannot do these three things well, you will not be a great CEO.