Unexpected increases of natural resource prices can generate rents, value that should be recovered by the State to minimize inefficiencies, avoid arbitrary discrimination between citizens and keep a sustainable trajectory. As a case study about private appropriation of natural resource rent, this work explores the case of copper in Chile since 1990, empirically analyzing if the 12 main private mining companies have recovered in present value more than their investment during their life cycle. The results of this exercise, applicable to other natural resources, indicate that some actually have, capturing about US$40 billion up to 2012. Elaborating an adequate institutional framework for future deposits remain important challenges for Chile to plentifully take advantage of its mining potential, as well as for any country with an abundant resource base to better enjoy its natural wealth. For that purpose, a concession known as Least Present Value Revenue (LPVR) is proposed.