  We consider current shot noise and the full counting statistics in a chain of
quantum dots which exhibits a continuous non-equilibrium phase transition as a
function of the tunnel couplings of the chain with the electrodes. Using a
combination of analytical and numerical methods, we establish that the full
counting statistics is conventional away from the phase transition, but
becomes, in a well-defined sense, essentially non-Gaussian on the critical
line, where the current fluctuations are controlled by the dynamic critical
exponent $z$. We find that signatures of the critical full counting statistics
persist in quantum-dot chains of finite length.
