Superconductivity in compressed lithium is observed by magnetic susceptibility and electrical resistivity measurements. A superconducting critical temperature (Tc) is found ranging from 9 to 16 kelvin at 23 to 80 gigapascals. The pressure dependence of Tc suggests multiple phase transitions, consistent with theoretical predictions and reported x-ray diffraction results. The observed values for Tc are much lower than those theoretically predicted, indicating that more sophisticated theoretical treatments similar to those proposed for metallic hydrogen may be required to understand superconductivity in dense phases of lithium.