This study is a Phase I trial to determine the safety of autologous mononuclear cells (MNC) derived from umbilical cord blood for intramyocardial delivery into the right ventricle during a planned and non-emergent Stage II surgical palliation in subjects with HLHS. This is the first critical step towards applying autologous MNC therapy as an add-on regenerative intervention for congenital heart disease management. The choice of HLHS as the target disease for regenerative therapies in congenital heart disease management is multi-factorial and includes the following considerations: 1) Severity of of this incurable disease, 2) palliative nature and burden of long-term outcomes with a single right ventricular system, 3) three stages of planned surgical procedures that provide time points to adjunctively intervene, and 4) prenatal diagnosis enabling planned collection of UCB. An emerging goal for cardiac regeneration includes the application of cell-based technology to congenital heart disease, which is a favorable substrate due to the lack of fibrotic scaring, and the presence of a microenvironment that is expected to support ongoing cardiac proliferation and growth for functional remuscularization. This Phase I safety study will determine the feasibility of collection, processing, and delivery of autologous cells as used in adult cardiac regenerative protocols in the setting of HLHS surgical management.