Participation in this study, including follow-up visits and phone calls, will last 60 months. Participants will first undergo 3 to 4 days of screening procedures that will include a physical examination, multiple lab tests, and a battery of tests on heart health. Next, participants will be randomized to receive either active stem cell injections or placebo injections. The injections and related procedures will be performed in a hospital and last approximately 72 hours. During this time, participants in both groups will first undergo a bone marrow aspiration procedure. Participants receiving active stem cells will also undergo NOGA electromechanical cardiac mapping, which involves inserting a monitoring device through a catheter and into the heart. Injections of stem cells will then be made to 15 damaged sites on the heart through a special catheter. Participants receiving placebo injections will receive 15 injections of an inactive, saline-based solution. After the injection procedures, all participants will undergo two echocardiograms, an electrocardiogram, blood tests, and overnight monitoring in a telemetry unit.