  The vacuum Einstein equations in five dimensions are shown to admit a
solution describing an asymptotically flat spacetime regular on and outside an
event horizon of topology S^1 x S^2. It describes a rotating ``black ring''.
This is the first example of an asymptotically flat vacuum solution with an
event horizon of non-spherical topology. There is a range of values for the
mass and angular momentum for which there exist two black ring solutions as
well as a black hole solution. Therefore the uniqueness theorems valid in four
dimensions do not have simple higher dimensional generalizations. It is
suggested that increasing the spin of a five dimensional black hole beyond a
critical value results in a transition to a black ring, which can have an
arbitrarily large angular momentum for a given mass.
