Covalent bonding is commonly described by Lewis's theory, with an electron pair shared between two atoms constituting one full bond. Beginning with the valence bond description for the hydrogen molecule, quantum chemists have further explored the fundamental nature of the chemical bond for atoms throughout the periodic table, confirming that most molecules are indeed held together by one electron pair for each bond. But more complex binding may occur when large numbers of atomic orbitals can participate in bond formation. Such behaviour is common with transition metals. When involving heavy actinide elements, metal-metal bonds might prove particularly complicated. To date, evidence for actinide-actinide bonds is restricted to the matrix-isolation of uranium hydrides, including H2U-UH2, and the gas-phase detection and preliminary theoretical study of the uranium molecule, U2. Here we report quantum chemical calculations on U2, showing that, although the strength of the U2 bond is comparable to that of other multiple bonds between transition metals, the bonding pattern is unique. We find that the molecule contains three electron-pair bonds and four one-electron bonds (that is, 10 bonding electrons, corresponding to a quintuple bond), and two ferromagnetically coupled electrons localized on one U atom each-so all known covalent bonding types are contributing.