  A sequence of zero-temperature black-hole spacetimes with angular momentum
and electric and magnetic charges is shown to exist in gauged $N=2$
supergravity. Stability of a subset of these spacetimes is demonstrated by
saturation of the Bogomol'nyi bound arising from the supersymmetry algebra. The
mass of the resulting solitonic black holes is given in terms of the
cosmological constant and the angular momentum. We conjecture that at the
quantum level these solitons are dyons with angular momentum determined by the
electric and magnetic charges.
