Thin films (0-30 nm) of very concentrated aqueous monovalent salt solutions (2-10 M of LiCl, NaCl, and CsCl) were examined to determine how ionic strength affects the screening length of the electrostatic potential. Measurements were consistent with a screening length in the range of 3-12 nm. The screening length increased monotonically as a function of salt concentration, and the rate of increase was a function of the monovalent salt type. The results were incompatible with the Debye length of Poisson-Boltzmann theory but consistent with previous measurements of surface forces. The screening length was determined from the surface excess of fluorescein, a dianion under basic conditions, which was present in trace amounts in the thin film and detected via its fluorescence emission. That is, we directly observed that the ion concentration in very concentrated solutions is perturbed far from an interface.