In this letter we present a hard x-ray phase contrast microscope based on the divergent and coherent beam exiting an x-ray waveguide. It uses lensless geometrical projection to magnify spatial variations in optical path length more than 700 times. Images of a nylon fiber and a gold test pattern were obtained with a resolution of 0.14 &mgr;m in one direction. Exposure times as short as 0.1 s gave already visible contrast, opening the way to high resolution, real time studies. ©1997 American Institute of Physics.