The coronavirus SARS-CoV-2 is cause of a global pandemic of a pneumonia-like disease termed Coronavirus Disease 2019 (COVID-19). COVID-19 presents a high mortality rate, estimated at 3.4%. More than 1 out of 4 hospitalized COVID-19 patients require admission to an Intensive Care Unit (ICU) for respiratory support, and a large proportion of these ICU-COVID-19 patients, between 17% and 46%, have died. In these patients COVID-19 infection causes an inflammatory response in the lungs that can progress to inflammation with cytokine storm, Acute Lung Injury (ALI), Acute Respiratory Distress Syndrome (ARDS), thromboembolic events, disseminated intravascular coagulation, organ failure, and death. Mesenchymal Stem Cells (MSCs) are potent immunomodulatory cells that recognize sites of injury, limit effector T cell reactions, and positively modulate regulatory cell populations. MSCs also stimulate local tissue regeneration via paracrine effects inducing angiogenic, anti-fibrotic and remodeling responses. MSCs can be derived in large number from the Umbilical Cord (UC). UC-MSCs, utilized in the allogeneic setting, have demonstrated safety and efficacy in clinical trials for a number of disease conditions including inflammatory and immune-based diseases. UC-MSCs have been shown to inhibit inflammation and fibrosis in the lungs and have been utilized to treat patients with severe COVID-19 in pilot, uncontrolled clinical trials, that reported promising results. UC-MSCs processed at our facility have been authorized by the FDA for clinical trials in patients with an Alzheimer's Disease, and in patients with Type 1 Diabetes (T1D). We hypothesize that UC-MSC will also exert beneficial therapeutic effects in COVID-19 patients with cytokine storm and ARDS. We propose an early phase controlled, randomized clinical trial in COVID-19 patients with ALI/ARDS. Subjects in the treatment group will be treated with two doses of UC-MSC (l00 × 10 cells). The first dose will be infused within 24 hours following study enrollment. A second dose will be administered 72 ± 6 hours after the first infusion. Subject in the control group will receive infusion of vehicle (DPBS supplemented with 1% HSA and 70 U/kg unfractionated Heparin, delivered IV) following the same timeline. Subjects will be evaluated daily during the first 6 days, then at 14, 28, 60, and 90 days following enrollment (see Schedule of Assessment for time window details). Safety will be determined by adverse events (AEs) and serious adverse events (SAEs) during the follow-up period. Efficacy will be defined by clinical outcomes, as well as a variety of pulmonary, biochemical and immunological tests. Success of the current study will provide a framework for larger controlled, randomized clinical trials and a means of accelerating a possible solution for this urgent but unmet medical need. The proposed early phase clinical trial will be performed at the University of Miami (UM), in the facilities of the Diabetes Research Institute (DRI), UHealth Intensive Care Unit (ICU) and the Clinical Translational Research Site (CTRS) at the University of Miami Miller School of Medicine and at the Jackson Memorial Hospital (JMH).