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