  Shot noise measures out-of-equilibrium current fluctuations and is a powerful
tool to probe the nature of current-carrying excitations in quantum systems.
Recent shot noise measurements in the heavy fermion strange metal
YbRh$_2$Si$_2$ exhibit a strong suppression of the Fano factor ($F$) -- the
ratio of the current noise to the average current in the DC limit. This system
is representative of metals in which electron correlations are extremely
strong. Here we carry out the first theoretical study on the shot noise of
diffusive metals in the regime of strong correlations. A Boltzmann-Langevin
equation formulation is constructed in a quasiparticle description in the
presence of strong correlations. We find that $F = \sqrt{ 3}/{4}$ in such a
correlation regime. Hence, the Fano factor suppression observed in experiments
on YbRh$_2$Si$_2$ necessitates a loss of the quasiparticles. Our work opens the
door to systematic theoretical studies of shot noise as a means of
characterizing strongly correlated metallic phases and materials.
