This study is being done on patients who have heart failure, a condition where the heart muscle weakens and enlarges and cannot pump blood effectively. The purpose of this study is to assess the safety and effectiveness of a new device called the AccuCinch Ventricular Restoration System and compare it to treatment with standard heart failure medications alone. The AccuCinch Ventricular Restoration System consists of anchors, which attach to your heart muscle, sliders to connect the anchors and a thread like cord that goes through the anchors and is cinched to make your enlarged heart smaller so it can pump more efficiently. The device is implanted in one of the lower pumping chambers of the heart (called left ventricle). The study will have two groups, the treatment group in which participants undergo the device implant in addition to taking heart failure medications and the control group in which participants are treated with heart failure medications alone. Participation will last up to 5 years.