This trial aims to determine the safety and effectiveness of using donated mesenchymal precursor cells following a heart attack. The trial is being conducted in 11 countries and is sponsored by Mesoblast Inc. To be included in the trial the damage to the heart (the infarct) must involve either some or complete blockage of the left coronary artery (referred to as ST-elevation myocardial infarction) and require treatment. Participants will be randomly divided into three groups. The first group will receive standard treatment (control group). The other two groups will receive different doses of mesenchymal precursor cell obtained from donated bone marrow. Participants will be monitored for complications and assessed in heart function. The trial expects to enrol 225 participants by March 2015.