A CEO does only three things. Sets the overall vision and strategy of the company and communicates it to all stakeholders. Recruits, hires, and retains the very best talent for the company. Makes sure there is always enough cash in the bank.

I would have to add a couple of things to this list, perhaps because I'm naive...

1) Stay ahead of your competition. Don't become complacent and let your competitors out-innovate you and crush you. This goes beyond "communicating" your vision. This is about having one.

2) Listen to your customers. Maybe some wouldn't consider this a CEO's priority, but I do. How is your company and product perceived by your harshest critics and most valuable asset and easiest/cheapest marketers?

Both of these fall under the general title of "keeping your finger on the pulse" and even more generally, "strategy". It perhaps belies my recent roles that I consider these elements a CEO priority. But, um, don't you?

If you want to lump these in with "setting the overall vision", then fine - we're on the same page.