The manipulation of fast moving, delicate tissues in beating heart procedures presents a considerable challenge to surgeons. We present a new robotic force stabilization system that assists surgeons by maintaining a constant contact force with the beating heart. The system incorporates a novel, miniature uniaxial force sensor that is mounted to surgical instrumentation to measure contact forces during surgical manipulation. Using this sensor in conjunction with real-time tissue motion information derived from 3D ultrasound, we show that a force controller with feed-forward motion terms can provide safe and accurate force stabilization in an in vivo contact task against the beating mitral valve annulus. This confers a 50% reduction in force fluctuations when compared to a standard force controller and a 75% reduction in fluctuations when compared to manual attempts to maintain the same force.