We derive a formula for the mean-square number fluctuation of counterions condensed on a polyion. The local average concentration of condensed counterions tends toward a finite value greater than zero as the charge density of the polyion tends from above toward its critical value, but the concentration fluctuations increase without bound. As an exercise in the application of the formula, we calculate the mean-square fluctuating dipole moment and, thereby, recover a previously derived formula for the static low-field polarizability of the condensed counterions.