  The known BPS dyon black hole solutions of the N=4 heterotic string in four
dimensions with non-zero angular momentum all have naked singularities. We show
that it is possible to modify a certain class of these solutions by the
addition of massive Kaluza-Klein fields in such a way that the solutions
decompactify near the core to five-dimensional black hole solutions with
regular event horizons. We argue that the degeneracy of the four-dimensional
BPS dyon states is given, for large charges, by the five-dimensional geometric
entropy.
