The supply of copper underpins global economic growth and human development. Forecasts predict a market deficit of 600 kilotones of copper metal by 2021. Accessing new and undeveloped copper orebodies is critical to meeting projected demand. The mining industry has historically addressed supply challenges by capitalising on rising metal prices. We test the assumption that a price rise will ‘unlock’ previously uneconomic orebodies. It is argued that reacting to a simple price rise is instead likely to ‘unleash’ an unacceptable suite of environmental and social impacts. This paper examines 308 of the world's largest undeveloped copper orebodies and provides a current, comprehensive, multi-factor risk profile of the world's future copper supply. Our analysis reveals that a significant proportion of future copper supply involves factors that are not immediately price-sensitive, and that a rapid unlocking of these ore bodies could have negative ramifications for economic growth, human development, and the transition to a low carbon future.