A new hydrodynamic instability is identified for a nanofluidic flow. The flow analyzed is an electro-osmotic flow of a thin liquid layer, bounded below by a solid substrate and above by an inert gas. The Debye-Huckel approximation is used for the potential distribution, and the interface with the gas is treated as a moving boundary. The stability analysis shows that the flow is always unstable to small-wavenumber disturbances, and the instability is accompanied by interface deformations. Neutral stability bounds due to the capillary cut-off are presented in parametric spaces for the electric field strength and the Debye length of the electrolyte.