When he walks into a room, Rex Tillerson radiates competence and stability. In a world grown weary of the shenanigans of energy companies like Enron, the oilman commands respect--and earns it--by pumping twice as much oil out of the ground as Kuwait does. As ExxonMobil's senior vice president for exploration and production, he was responsible for 80% of the $11 billion profit generated last year by the world's largest private oil company. The challenge: Can Tillerson, 51, ride that success to become CEO?
ExxonMobil's reigning chief, Lee Raymond, 65, has extended his stay on the job ostensibly to handle fallout from...