Magnetic resonance imaging (MRI) is a powerful imaging technique that typically operates on the scale of millimetres to micrometres. Conventional MRI is based on the manipulation of nuclear spins with radio-frequency fields, and the subsequent detection of spins with induction-based techniques. An alternative approach, magnetic resonance force microscopy (MRFM), uses force detection to overcome the sensitivity limitations of conventional MRI. Here, we show that the two-dimensional imaging of nuclear spins can be extended to a spatial resolution better than 100 nm using MRFM. The imaging of F-19 nuclei in a patterned CaF2 test object was enabled by a detection sensitivity of roughly 1,200 nuclear spins at a temperature of 600 mK. To achieve this sensitivity, we developed high-moment magnetic tips that produced field gradients up to 1.4 x 10(6) Tm-1, and implemented a measurement protocol based on force-gradient detection of naturally occurring spin fluctuations. The resulting detection volume was less than 650 zeptolitres. This is 60,000 times smaller than the previous smallest volume for nuclear magnetic resonance microscopy, and demonstrates the feasibility of pushing MRI into the nanoscale regime.