  It is known that the number of points in the largest cluster of a percolating
Poisson process restricted to a large finite box is asymptotically normal. In
this note, we establish a rate of convergence for the statement. As each point
in the largest cluster is determined by points as far as the diameter of the
box, known results in the literature of normal approximation for Poisson
functionals cannot be directly applied. To disentangle the long-range
dependence of the largest cluster, we use the fact that the second largest
cluster has comparatively shorter range of dependence to restrict the range of
dependence, apply a recently established result in Chen, R\"ollin and Xia
(2021) to obtain a Berry-Esseen type bound for the normal approximation of the
number of points belonging to clusters that have a restricted range of
dependence, and then estimate the gap between this quantity and the number of
points in the largest cluster.
