X-ray tomography is a ubiquitous tool used, for example, in medical diagnosis, explosives detection or to check structural integrity of complex engineered components. Conventional tomographic images are formed by measuring many transmitted X-rays and later mathematically reconstructing the object, however the structural and chemical information carried by scattered X-rays of different wavelengths is not utilised in any way. We show how a very simple; laboratory-based; high energy X-ray system can capture these scattered X-rays to deliver 3D images with structural or chemical information in each voxel. This type of imaging can be used to separate and identify chemical species in bulk objects with no special sample preparation. We demonstrate the capability of hyperspectral imaging by examining an electronic device where we can clearly distinguish the atomic composition of the circuit board components in both fluorescence and transmission geometries. We are not only able to obtain attenuation contrast but also to image chemical variations in the object, potentially opening up a very wide range of applications from security to medical diagnostics.