Economic growth over the past 40 years has used increasing quantities of fossil energy, and most importantly oil. Yet, our ability to increase the global supply of conventional crude oil much beyond current levels is doubtful, which may pose a problem for continued economic growth. Our research indicates that, due to the depletion of conventional, and hence cheap, crude oil supplies (i.e., peak oil), increasing the supply of oil in the future would require exploiting lower quality resources (i.e., expensive), and thus could occur only at high prices. This situation creates a system of feedbacks that can be aptly described as an economic growth paradox: increasing the oil supply to support economic growth will require high oil prices that will undermine that economic growth. From this we conclude that the economic growth of the past 40 years is unlikely to continue in the long term unless there is some remarkable change in how we manage our economy.