In the light of the tremendous progress that has been made in raising the transition temperature of the copper oxide superconductors (for a review, see ref. 1), it is natural to wonder how high the transition temperature, Tc, can be pushed in other classes of materials. At present, the highest reported values of T-c for non-copper-oxide bulk superconductivity are 33 K in electron-doped CsxRbyC60 (ref. 2), and 30 K in Ba1-xKxBiO3 (ref. 3). (Hole-doped C-60 was recently found(4) to be superconducting with a T-c as high as 52 K, although the nature of the experiment meant that the supercurrents were confined to the surface of the C-60 crystal, rather than probing the bulk.) Here we report the discovery of bulk superconductivity in magnesium diboride, MgB2. Magnetization and resistivity measurements establish a transition temperature of 39 K, which we believe to be the highest yet determined for a non-copper-oxide bulk superconductor.