The Dirac equation describes the relativistic evolution of electrons and positrons.  We consider the (time-dependent!) Dirac equation in three dimensions coupled to a potential with Coulomb-type singularities.  We prove a propagation of singularities result for this equation and show that singularities are diffracted by the singularities of the potential.  We finally compute the symbol of the diffracted wave and show it is typically non-zero.  This talk is based on joint work with Jared Wunsch.