Superconductivity at high temperatures is expected in elements with low atomic numbers, based in part on conventional BCS (Bardeen-Cooper-Schrieffer) theory. For example, it has been predicted that when hydrogen is compressed to its dense metallic phase (at pressures exceeding 400 GPa), it will become superconducting with a transition temperature above room temperature. Such pressures are difficult to produce in a laboratory setting, so the predictions are not easily confirmed. Under normal conditions lithium is the lightest metal of all the elements, and may become superconducting at lower pressures; a tentative observation of a superconducting transition in Li has been previously reported. Here we show that Li becomes superconducting at pressures greater than 30 GPa, with a pressure-dependent transition temperature (T(c)) of 20 K at 48 GPa. This is the highest observed T(c) of any element; it confirms the expectation that elements with low atomic numbers will have high transition temperatures, and suggests that metallic hydrogen will have a very high T(c). Our results confirm that the earlier tentative claim of superconductivity in Li was correct.