The scanning tunneling microscope (STM) has been employed to induce defects, having dimensions of 100-200 Angstrom, in bilayers of stearic acid or cadmium stearate supported on a graphite surface. Defect formation followed the application of a bias pulse between the STM tip and surface. Cylindrical voids or "pores", formed by this process, gradually refilled the approximate to 10 min following formation. From STM images of pore refilling, a hydrodynamic momentum equation-derived here-enabled the calculation of a viscosity of 2.6 Pa s m for a cadmium stearate bilayer. This measurement suggests that the STM provides a means for measuring the viscosity of nanometer-scale regions of supported molecular assemblies.