  We present a new supersymmetric, asymptotically flat, black hole solution to
five-dimensional U(1)^3-supergravity which is regular on and outside an event
horizon of lens space topology L(2,1). The solution has seven independent
parameters and uplifts to a family of 1/8-supersymmetric D1-D5-P black brane
solutions to Type IIB supergravity. The decoupling limit is asymptotically
AdS(3) x S^3 x T^4, with a near-horizon geometry that is a twisted product of
the near-horizon geometry of the extremal BTZ black hole and L(2,1) x T^4,
although it is not (locally) a product space in the bulk. We show that the
decoupling limit of a special case of the black lens is related to that of a
black ring by spectral flow, thereby supplying an account of its entropy.
Analogous solutions of U(1)^N-supergravity are also presented.
