Microstates of the D1-D5-Kaluza-Klein monopole system

We find supergravity solutions corresponding to all U(1)xU(1) invariant chiral primaries of the D1-D5-KK system. These solutions are 1/8 BPS, carry angular momentum, and are asymptotically flat in the 3+1 dimensional sense. They can be thought of as representing the ground states of the four-dimensional black hole constructed from the D1-D5-KK-P system. Demanding the absence of unphysical singularities in our solutions determines all free parameters, and gives precise agreement with the quantum numbers expected from the CFT point of view. The physical mechanism behind the smoothness of the solutions is that the D1 branes and D5 branes expand into a KK-monopole supertube in the transverse space of the original KK monopole.