Hard X-ray phase microscopy using the Speckle Tracking technique is presented and the practical implementation of this microscope explained. It is demonstrated that the spatial resolution of the Speckle Tracking technique can be pushed down to the nanometer scale without sacrificing the angular sensitivity, which is in the tens of nanoradians range. Moreover, the method is suitable for the analysis of dynamic samples. Experimental demonstration of the method is given for the case of phase imaging of micrometer size polystyrene spheres using a Fresnel zone plate as a magnifying optical element. (C) 2013 AIP Publishing LLC [http://dx.doi.org/10.1063/1.4802729]