FOLLOWING the discovery1 of high-transition-temperature (high-Tc) superconductivity in doped La2CuO4, several families of related compounds have been discovered which have layers of CuO2 as the essential requirement for superconductivity: the highest transition temperatures so far have been found for thallium-bearing compounds2. Recently the mercury-bearing compound HgBa 2Rcu2O6+δ (Hg-1212) was synthesized 3 (where R is a rare-earth element), with a structure similar to the thallium-bearing superconductor TlBa2CaCu2O7 (Tl-1212), which has one T1O layer and two CuO2 layers per unit cell, and a Tc of 85 K (ref. 2). But in spite of its resemblance to Tl-1212, Hg-1212 was found not to be superconducting. Here we report the synthesis of the related compound HgBa2CuO4+δ (Hg-1201), with only one CuO2 layer per unit cell, and show that it is superconducting below 94 K. Its structure is similar to that of Tl-1201 (which has a Tc of < 10 K)4, but its transition temperature is considerably higher. The availability of a material with high Tc but only a single metal oxide (HgO) layer may be important for technological applications, as it seems that a smaller spacing between CuO 2 planes leads to better superconducting properties in a magnetic field5.