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 that cryopreservation and intra-myocardial delivery of one billion hESC-CMs generates extensive remuscularization of the infarcted heart.