A system is provided for fastening an implantable medical device, for example a defibrillator lead, to the heart. A lead electrode is placed in a desired position against the pericardium, pericardial tissue is grasped with a fastening tool, and the pericardial tissue is drawn away from epicardium and toward the fastening tool. A fastening member is applied to the pericardial tissue and to the lead electrode to secure the lead in the desired position. The application tool comprises a first pair of jaws for grasping membranous tissue and drawing the tissue away from other tissues and toward the tool. A second pair of jaws is provided for holding fastener members and delivering the fastener members to the membranous tissue.