  We examine Hubeny's scenario according to which a near-extremal
Reissner-Nordstr\"om black hole can absorb a particle and be driven toward an
over-extremal state in which the charge exceeds the mass, signaling the
destruction of the black hole. Our analysis incorporates the particle's
electromagnetic self-force and the energy radiated to infinity in the form of
electromagnetic waves. With these essential ingredients, our sampling of the
parameter space reveals no instances of an overcharged final state, and we
conjecture that the self-force acts as a cosmic censor, preventing the
destruction of a near-extremal black hole by the absorption of a charged
particle. We argue, on the basis of the third law of black-hole mechanics, that
this conclusion is robust and should apply to attempts to overspin a Kerr black
hole.
