A chief executive had a dilemma. After working in a fast-growing company as COO, he accepted an offer from venture capitalists to start his own company. Within five years he had built a new enterprise generating revenues over $300 million and profit margins so high that his company had compiled a substantial cash reserve with which it was poised to go on an acquisition run. His passion, strategic and analytical brilliance, and relentless focus on practical results made him a rare, virtually unstoppable force in industry.

So what was his problem? He was irreplaceable, at least according to his board. It was the board’s fundamental responsibility to protect the shareholders’ interests with a viable succession plan, and for this they simply had no acceptable answer. They demanded that he find a solution.

He asked me for counsel:

Justin, I have two people on my team that I think can grow into my role. But my board vehemently disagrees and thinks I vastly overestimate their long-term potential to actually run a company. They’re both superstars. How do I know which one — or if either one — can make the leap, or whether this is just a pipe dream that’s going to waste a lot of time, money, and focus?

It’s a good question, one I’m often asked. How do you know when someone can make the leap from high performer to CEO? There is one driving factor that determines the answer: narcissism.

Those selected for development have one universal trait in common: They are by definition high achievers. But there is a difference between those superstar achievers that can make the leap to CEO and those that will implode: To what degree do they feel invigorated by the success and talent of others, and to what degree does the success of others cause an involuntary pinch of insecurity about their own personal inadequacies? Only an individual who feels genuinely invigorated by the growth, development, and success of others can become an effective leader of an enterprise. And it remains the most common obstacle of success for those trying to make that leap.

There is powerful evidence (pdf) that narcissists have difficulty forging long-term relationships. Because narcissists are continuously seeking recognition from others to reinforce their own self-worth, they tend to form new relationships where they can see a positive reflection of themselves in the other person’s eye. However, because of their obsession with analyzing events around them to see what they suggest about their own identities, they also exhaust those relationships. In leadership positions, this leaves colleagues feeling like collective efforts are being used to increase a single narcissist leader’s ego, rather than a team’s shared goals.

Keeping an eye on the high achiever’s relationships and self-promotion certainly helps to see if your candidate is a narcissist. The Narcissistic Personality Inventory also has several questions that suggest how to further clarify an individual’s level of narcissism, including:

Are the individual’s relationships with others based on honest, intimate exchanges, or are they formed using a dynamic that regularly reinforces the narcissist’s role as a “hero”?

Does the individual often talk about how his star qualities make him distinct from his peers?

Does he like to be the center of attention?

Does the remark, “I insist on getting the respect that is due me,” resonate with his worldview?

If you answered “yes” to many of the questions above, chances are you’re describing a high achiever who possesses a costly level of narcissism. But there are ways to help these individuals make the leap from high achievers to leaders.

First, coach them to continuously attribute credit to others for any successful project. Point out how this will produce long-term rewards because others will see that the projects they’re responsible for produce successful outcomes. In the end, other talented people will vie to work with them and give them their best, further improving their track records of disseminating success.

Then, press hard against any behaviors that self-aggrandize. Frame the lesson in a language that high achievers can understand: If their intent is to get ahead, self-promotion is likely doing just the opposite over the long term. It is in their self-interest to change.

Individuals with extreme levels of insecurity — those that cannot remain stable while seeing others succeed — will fail in leadership. In these cases, you may need to arrange psychological interventions that get to the root of their insecurities and help them heal if they are to become successful leaders.

While elevated narcissism and self-promotion has been shown to result in quicker promotion early in one’s career, its negative impacts are revealed in positions of higher authority. In these positions, blind ambition becomes its own worst enemy. In identifying these traits early and combating them through mentorship, you can transform these high achievers into quality leaders.