A linearized stability analysis is carried out for an evaporating liquid surface with a view of understanding some observations with highly superheated liquids. The analytical results of this study depend on the unperturbed temperature near the liquid surface. The absence of this data renders a comparison with experiment impossible. However, on the basis of several different assumptions for this temperature distribution, instabilities of the interface of a rapidly evaporating liquid are found for a range of wavenumbers of the surface wave perturbation. At large evaporating mass flow rates the instability is very strong with growth times of a millisecond or less. A discussion of the physical mechanism leading to the instability is given.