Micromechanical sensing of magnetic force was used to detect nuclear magnetic resonance with exceptional sensitivity and spatial resolution. The results suggest that magnetic force sensing is a viable approach for enhancing the sensitivity and spatial resolution of nuclear magnetic resonance microimaging. The envisioned "magnetic resonance force microscope" would have elemental identification capability and be able to determine nuclear positions with subangstrom spatial resolution in three dimensions. Such an instrument, if it could be built, would represent a revolutionary advance for the field of magnetic resonance imaging and would greatly facilitate the determination of molecular structures.