A clinical program for X-ray phase contrast (PhC) mammography with synchrotron radiation (SR) has been started in March 2006 at the SYRMEP beamline of Elettra, the SR facility in Trieste, Italy. The original beamline layout has been modified substantially and a clinical facility has been realized. In order to fulfill all security requirements, dedicated systems have been designed and implemented, following redundancy criteria and "fail safe" philosophy. Planar radiographic images are obtained by scanning simultaneously the patient and the detector through the stationary and laminar SR beam. In this first phase of the project a commercial screen-film system has been used as image receptor. Upon approval by the respective authorities, the mammography program is about half way to conclusion. Up to now about 50 patients have been examined. The patients are volunteers recruited by the radiologist after conventional examinations at the hospital resulted in an uncertain diagnosis. As an example one case of PhC SR mammography is shown and compared to conventional digital mammography. Preliminary analysis shows the high diagnostic quality of the PhC SR images that were acquired with equal or less delivered dose compared to the conventional ones.