Plutonium is a metal of both technological relevance and fundamental scientific interest. Nevertheless, the electronic structure of plutonium, which directly influences its metallurgical properties, is poorly understood. For example, plutonium's 5f electrons are poised on the border between localized and itinerant, and their theoretical treatment pushes the limits of current electronic structure calculations. Here we extend the range of complexity exhibited by plutonium with the discovery of superconductivity in PuCoGa5. We argue that the observed superconductivity results directly from plutonium's anomalous electronic properties and as such serves as a bridge between two classes of spin-fluctuation-mediated superconductors: the known heavy-fermion superconductors and the high-T(c) copper oxides. We suggest that the mechanism of superconductivity is unconventional; seen in that context, the fact that the transition temperature, T(c) approximately 18.5 K, is an order of magnitude greater than the maximum seen in the U- and Ce-based heavy-fermion systems may be natural. The large critical current displayed by PuCoGa5, which comes from radiation-induced self damage that creates pinning centres, would be of technological importance for applied superconductivity if the hazardous material plutonium were not a constituent.