The high price of oil presents the leaders of the Gulf Cooperation Council (GCC) states—Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates (UAE)—with a singular opportunity to diversify their economies beyond hydrocarbons. How they manage that opportunity has far-reaching implications not only for their own populations but also for the entire global economy.

The challenge before these leaders is substantial. Unemployment is high, particularly among the young, and in the years ahead the GCC states must create millions of new private-sector jobs. Doing so will require crucial reforms to labor markets and to financial and educational systems.

Can the GCC states do it? Skeptics, noting that countries rich in natural resources—especially oil—often struggle to manage their wealth, argue that the current high prices actually present an impediment to reform. We have a different view: given the growing pressure within the GCC states to reduce unemployment and provide jobs for an unusually young labor force, oil revenues will serve as a catalyst to continue the reforms needed to break away from the boom-and-bust cycles that volatile energy prices create.

Already, the region’s dynamism has fostered some noticeable changes, evident in areas as diverse as the Dubai skyline and...