  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 {\em 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 neutron star mergers. The cCBC
signal is clean in a BH-NS merger with a small mass ratio ($q \equiv m_2/m_1 <
0.2$), 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 (EMRIs)
is also estimated.
