Elements in the alkali metal series are regarded as unlikely superconductors because of their monovalent character. A superconducting transition temperature as high as 20 K, recently found in compressed lithium (the lightest alkali element), probably arises from pressure-induced changes in the conduction-electron band structure. Superconductivity at ambient pressure in lithium has hitherto remained unresolved, both theoretically and experimentally. Here we demonstrate that lithium is a superconductor at ambient pressure with a transition temperature of 0.4 mK. As lithium has a particularly simple conduction electron system, it represents an important case for any attempts to classify superconductors and transition temperatures, especially to determine if any non-magnetic configuration can exclude superconductivity down to zero temperature. Furthermore, the combination of extremely weak superconductivity and relatively strong nuclear magnetism in lithium would clearly lead to mutual competition between these two ordering phenomena under suitably prepared conditions.