Using a modified atomic force microscope (AFM) with a conducting cantilever, we have investigated the dielectric strength of SiO2 gate oxide films. This has been achieved by spatially resolving the prebreakdown tunneling current flowing between the silicon substrate and tip. During AFM imaging a voltage ramp was applied to the tip at each image point so as to determine the local threshold voltage required to generate a small tunneling current in the oxide, without causing an irreversible electrical breakdown. For an oxide 12-nm thick this voltage was found to vary by more than a factor of 2.7 over an area of 0.14 mum2, with a maximum value of 40.5 V. This suggests that the breakdown strength of conventional metal-oxide-silicon capacitors may not be limited by the intrinsic dielectric strength of the oxide, but by imperfections or nonuniformities in the Si/SiO2 structure. By preventing irreversible oxide breakdown during scanning, we can image the dielectric properties of oxide films with a lateral resolution better than 20 nm.