A new supersymmetric black hole solution of five-dimensional supergravity is presented. It has an event horizon of topology S1 X S2. This is the first example of a supersymmetric, asymptotically flat black hole of nonspherical topology. The solution is uniquely specified by its electric charge and two independent angular momenta. These conserved charges can be arbitrarily close, but not exactly equal, to those of a supersymmetric black hole of spherical topology.