Abstract: In this talk, I report on our computation of the electromagnetic self-force acting on a charged particle in the vicinity of a Reissner-Nordstrom black hole. This has implications on an apparent violation of cosmic censorship first identified by Hubeny, whereby a charged particle falling toward a nearly extremal Reissner-Nordstrom black hole can drive it beyond the extremal limit to form a naked singularity. However, the Hubeny analysis is at best tentative because it does not include the effect of the self-force acting on the falling charge. It is generally believed that the self-force is the mechanism by which nature ultimately avoids the Hubeny scenario, but this has never been sufficiently investigated. Our calculation will shed light on the question of just how effectively the self-force can act as a cosmic censor.