The purpose of this study was to explore the potential of refraction contrast X-ray imaging of biological tissues. Images of dissected mouse lungs, heart, liver and legs were produced using the medical beamline at the Elettra Synchrotron at Trieste, Italy. The technique used was diffraction enhanced imaging. This utilizes a silicon crystal positioned between the tissue sample and the detector to separate refracted X-rays from transmitted and scattered radiation by Bragg diffraction. The contrast in the images produced is related to changes in the X-ray refractive index of the tissues, resulting in remarkable clarity compared with conventional X-ray images based on absorption effects. These changes were greatest at the boundaries between different tissues, giving a marked edge enhancement effect and three-dimensional appearance to the images. The technique provides a way of imaging a property of biological tissues not yet exploited, and further studies are planned to identify specific applications in medical imaging.