Beating heart intracardiac procedures promise significant benefits for patients, however, the fast motion of the heart poses serious challenges to surgeons. We present a new 3D ultrasound-guided motion (3DUS) compensation system that synchronizes instrument motion with the heart. The system utilizes the fact that the motion of some intracardiac structures, including the mitral valve annulus, is largely constrained to translation along one axis. This allows the development of a real-time 3DUS tissue tracker which we integrate with a 1 degree-of-freedom actuated surgical instrument, real-time 3DUS instrument tracker, and predictive filter to devise a system with synchronization accuracy of 1.8 mm RMSE. User studies involving the deployment of surgical anchors in a simulated mitral annuloplasty procedure demonstrate that the system increases success rates by over 100%. Furthermore, it enables more careful anchor deployment by reducing forces to the tissue by 50% while allowing instruments to remain in contact with the tissue for longer periods.