In X-ray imaging, photons are transmitted through and absorbed by the target object, but are also scattered in significant quantities. Previous attempts to use scattered X-ray photons for imaging applications used pencil or fan beam illumination. Here we present 3D X-ray Scatter Tomography using full-field illumination for small-animal imaging. Synchrotron imaging experiments were performed on a phantom and the chest of a juvenile rat. Transmitted and scattered photons were simultaneously imaged with separate cameras; a scientific camera directly downstream of the sample stage, and a pixelated detector with a pinhole imaging system placed at 45° to the beam axis. We obtained scatter tomogram feature fidelity sufficient for segmentation of the lungs and major airways in the rat. The image contrast in the scatter tomogram slices approached that of transmission imaging, indicating robustness to the amount of multiple scattering present in our case. This opens the possibility of augmenting full-field 2D imaging systems with additional scatter detectors to obtain complementary modes or to improve the fidelity of existing images without additional dose, potentially leading to single-shot or reduced-angle tomography or overall dose reduction for live animal studies.