Using a temperature-dependent potential obtained from lattice gauge calculations, we study the stability of heavy quarkonia in the quark-gluon plasma. We find that only Υ(1S) and ηb(1S) are bound in the quark-gluon plasma, and have a small binding energy. The quark-gluon plasma may be revealed by an Υ(1S) dilepton peak with an invariant mass close to twice the current b quark mass, which is low...