If at least one of the members of a compact binary coalescence is charged, the inspiral of the two members would generate a Poynting flux with an increasing power, giving rise to a brief electromagnetic counterpart temporally associated with the chirp signal of the merger (with possibly a small temporal offset), which we term as the charged compact binary coalescence (cCBC) signal. We develop a general theory of cCBC for any mass and amount of charge for each member. Neutron stars (NSs), as spinning magnets, are guaranteed to be charged, so the cCBC signal should accompany all NS mergers. The cCBC signal is clean in a black hole (BH)-NS merger with a small mass ratio (q m m 0.2 2 1 º < ), in which the NS plunges into the BH as a whole, and its luminosity/energy can reach that of a fast radio burst if the NS is Crab-like. The strength of the cCBC signal in Extreme Mass Ratio Inspiral Systems is also estimated.2 1 º , where m 1 and m 2 <m 1 are the masses of the two members in the CBC. This is because the accretion-powered short GRB signal in these systems is orders of magnitude brighter than the cCBC signal. Furthermore, the dynamical ejecta launched during the merger places a