Pluripotent stem cells provide a potential solution to current epidemic rates of heart failure by providing human cardiomyocytes to support heart regeneration. Studies of human embryonic-stem-cell-derived cardiomyocytes (hESC-CMs) in small-animal models have shown favourable effects of this treatment. However, it remains unknown whether clinical-scale hESC-CM transplantation is feasible, safe or can provide sufficient myocardial regeneration. Here we show that hESC-CMs can be produced at a clinical scale (more than one billion cells per batch) and cryopreserved with good viability. Using a non-human primate model of myocardial ischaemia followed by reperfusion, we show that cryopreservation and intra-myocardial delivery of one billion hESC-CMs generates extensive remuscularization of the infarcted heart. The hESC-CMs showed progressive but incomplete maturation over a 3-month period. Grafts were perfused by host vasculature, and electromechanical junctions between graft and host myocytes were present within 2 weeks of engraftment. Importantly, grafts showed regular calcium transients that were synchronized to the host electrocardiogram, indicating electromechanical coupling. In contrast to small-animal models, non-fatal ventricular arrhythmias were observed in hESC-CM-engrafted primates. Thus, hESC-CMs can remuscularize substantial amounts of the infarcted monkey heart. Comparable remuscularization of a human heart should be possible, but potential arrhythmic complications need to be overcome.