The FRONTier RADiography (FRONTRAD) collaboration is developing a digital system for mammography at the Elettra Synchrotron Light Source in Trieste. The system is based on a silicon microstrip detector array. The ASIC FROST (FRONTRAD Read Out sySTem) was developed as a collaboration between INFN Trieste and Aurelia Microelettronica and is designed to operate in single photon counting mode. FROST provides low-noise and high-gain performances and is able to work at incident photon rates higher than 100 kHz with almost 100% efficiency. The ASIC has been tested and the first images of mammographic test objects will be shown. The acquisition time per breast image should be of about 10 s.