We demonstrate a new method whereby near-field optical microscope resolution can be extended to the nanometer regime. The technique is based on measuring the modulation of the scattered electric field from the end of a sharp silicon tip as it is stabilized and scanned in close proximity to a sample surface. Our initial results demonstrate resolution in the 3 nm range--comparable to what can be achieved with typical attractive mode atomic force microscopes. Theoretical considerations predict that the ultimate resolution achievable with this approach could be close to the atomic level.