We have developed a new X-ray imaging technique, diffraction enhanced imaging (DEI), which can be used to independently visualize the refraction and absorption of an object. The images are almost completely scatter-free, allowing enhanced contrast of objects that develop small angle scattering. The combination of these properties has resulted in images of mammography phantoms and tissues that have dramatically improved contrast over standard imaging techniques. This technique potentially is applicable to mammography and other fields of medical X-ray imaging and to radiology in general, as well as possible use in nondestructive testing and X-ray computed tomography. Images of various tissues and materials are presented to demonstrate the wide applicability of this technique to medical and biological imaging.