Background: Heart failure develops after myocardial infarction and is a major cause of morbidity and mortality. The ability to direct differentiation of embryonic stem cells (ESC) towards a cardiomyogenic phenotype makes them an attractive therapeutic option for cardiac repair, but species-specific and individual-specific immunological imprinting remains a hurdle. Our aim was to ascertain whether the purported immune privilege of ESC allows for their cross-species engraftment in a clinically relevant large-animal model. Methods: We studied engraftment and differentiation of cardiac-committed mouse ESC in 18 sheep in which a myocardial infarction had been induced; nine controls received medium and nine sheep (five of which were immunosuppressed) received ESC. The gain in myocardial function was measured by echocardiography 1 month after cell transplantation. Findings: Cardiac-committed murine ESC engrafted in infarcted myocardium of immunosuppressed and immunocompetent sheep, and differentiated into mature cardiomyocytes that expressed connexins. Colonisation of the scar area by ESC was accompanied by a functional benefit of the damaged myocardium. Left-ventricular ejection fraction deteriorated in the control group by a median of 9.9% (range -20 to 0.3) relative to baseline (p=0.011) whereas in the treated group it improved by 6.6% (-5.7 to 50.8; comparison between groups p=0.002). Interpretation: These findings obtained in a clinically relevant large-animal model of heart failure strengthen the potential therapeutic use of ESC to regenerate the severely dysfunctional myocardium and bring additional evidence for an immune privilege of these cells.