ELECTRIC-field-induced evaporation of ions from a needle-like surface, and their subsequent identification by time-of-flight mass spectrometry, forms the basis of the atom-probe technique1. This has proved to be a powerful analytical tool2,3, permitting the quantitative determination of material composition in a small selected region of the surface (depths of 1–5 nm) with single-layer resolution. Positional information for the atoms within each layer is lost, however. In contrast, the field-ion microscope3 provides atomic-resolution images of surfaces, but without information about the nature of the atoms. Several attempts have been made to combine these two techniques by extending the time-of-flight measurement into two dimensions, but they have been limited by their inability to identify all chemical species4 or to combine spatial and temporal information for multiple events5, especially for ions with very similar mass-to-charge ratios6. Here we make use of a recently developed7 multiple-impact detector to construct a position-sensitive atom probe with sufficiently high temporal resolution (of the order of 10 ns) to avoid these earlier problems; thus, reliable composition and position data can be obtained at the same time. We illustrate the performance of this instrument by imaging the three-dimensional distribution of chemical heterogeneities in a nickel-based alloy on a near-atomic scale.