High-mass stars may form by disk accretion like low-mass stars, but observational evidence for massive circumstellar disks remains sparse even after intense searches. We present Plateau de Bure observations of dust continuum and H218O line emission at 1.3 mm wavelength which show a rotating disk around the nearby (d=1 kpc) high-mass (L = 2 × 104 Lsol) protostar AFGL 2591. The 205 GHz map shows three sources. Comparison with OVRO 86 GHz images in- dicates that the strongest source is due to dust, while the other two are dominated by ionized gas. The dust source is compact (? ≍ 800 AU) and somewhat elongated (axis ratio ≍ 0.8). Its flux density indicates a mass of ≍ 0.8 Msol which is ≍ 5% of the mass of the central star. The dust opacity index β ≍ 1, suggesting grain growth. These observations suggest a disk at an inclination of ≍ 32◦ (almost face-on), but spectral line data are needed to test this idea. H218O line emission is only detected toward the dust source. The size and shape of the emission are very similar to that of the continuum. All of the single-dish line flux is recovered, so that there is probably little extended flux missing. Radiative transfer models indicate a H2O abundance of ~10-4, similar to the H2O ice abundance measured in the mid-infrared. The origin of the H2O thus seems to be evaporation of grain mantles. The position of the H218O emission peak shows a systematic shift with velocity. Such a gradient could arise in a bipolar outflow, but the high column densities (N(H2O) ~ 3 × 1019 cm-2; N(H2) ~ 2 × 1024 cm-2) argue against this. Moreover, the velocity gradient is not oriented East-West like the large-scale outflow from AFGL 2591. Thus the H218O velocity gradient probably traces a rotating disk. The magnitude of the velocity gradient is consistent with Keplerian rotation around the central star. In the near future, we plan to use more extended array configurations to resolve the velocity field.Read less <