Hyperspectral 3D imaging aims to acquire both depth and spectral information of a scene. However, existing methods are either prohibitively expensive and bulky or compromise on spectral and depth accuracy. In this work, we present Dispersed Structured Light (DSL), a cost-effective and compact method for accurate hyperspectral 3D imaging. DSL modifies a traditional projector-camera system by placing a sub-millimeter thick diffraction grating film front of the projector.The grating disperses structured light based on light wavelength. To utilize the dispersed structured light, we devise a model for dispersive projection image formation and a per-pixel hyperspectral 3D reconstruction method. We validate DSL by instantiating a compact experimental prototype.DSL achieves spectral accuracy of 18.8nm full-width half-maximum (FWHM) and depth error of 1mm. We demonstrate that DSL outperforms prior work on practical hyperspectral 3D imaging.DSL promises accurate and practical hyperspectral 3D imaging for diverse application domains, including computer vision and graphics, cultural heritage, geology, and biology.