Actually I have met two - in my seven years as a CEO and before that CCO in two different companies. I believe that the higher up you climb the more chance there is that you will meet a corporate psychopath.
My best advise to you is: GET OUT as fast as you can. You can not beat a psychopath, you can not live with a psychopath as a boss, so you'd better leave you job or ask for a transfer.
Psychopaths operate on a different level than you. They have no empathy and thus not a care in the World for you or your surroundings. They will push you, coerce you and make you struggle so they can look good in the eyes of the shareholders, the public or the top management. They are entirely scrupulous about exploiting you in your free time off work. They will invade your private sphere if it will help them reach their goal. And they will most likely play with your head, so you wind up thinking there is something wrong with you.
I had a Chairman of the Board that could never stop. He would send endless e-mails, he would be "surprised" and bewildered every time there was a conflict situation, where he would have to assume responsibility for a decision. He would go to extreme lengths to have all his bases covered, so the Board and the public owner would never be able to accuse him of a single mistake. Fault of the Management I believe the term is. A very well known term for most in management position. But nevertheless not a good feeling.
Your health is at stake when it comes to an unhealthy work environment, but this is even more true if you have a leader with no empathy or a leader with the traits of a psychopath. If you are keen to know more about the traits of a corporate psychopath, then read the book
The book gives you a good insight into strategies you can use to minimize the damage of dealing with a corporate psychopath - even if it is only for a short while.
Personally I hit an all-time low in my career and made some drastic changes in my professional life. Never again will I find myself stuck in a situation like that again. Then I would rather take any kind of job to be in a more healthy work environment. Food for thoughts? I hope so.