Shell model calculations are employed to estimate an upper limit of statistical fluctuations in the nuclear ground-state energies. In order to mimic the presence of quantum chaos associated with neutron resonances at energies between 6 and 10 MeV, calculations include random interactions in the upper shells. The upper bound for the energy fluctuations at mid-shell is shown to have the form σ(A)20 A-1.34 MeV. This estimate is consistent with the mass errors found in large-shell model calculations along the N=126 line, and with local mass error estimated using the Garvey–Kelson relations, all being smaller than 100 keV. It agrees in both size and functional form with the fluctuations deduced independently from second-order perturbation theory.