  We have experimentally investigated the quasiparticle shot noise in
NbN/MgO/NbN superconductor - insulator - superconductor tunnel junctions. The
observed shot noise is significantly larger than theoretically expected. We
attribute this to the occurrence of multiple Andreev reflection processes in
pinholes present in the MgO barrier. This mechanism causes the current to flow
in large charge quanta (Andreev clusters), with a voltage dependent average
value of m = 1+ 2 Delta/eV times the electron charge. Because of this charge
enhancement effect, the shot noise is increased by the factor m.
