Effective therapies are urgently needed for the SARS-CoV-2/COVID19 pandemic. We identified panels of fully human monoclonal antibodies (mAbs) from eight large phage-displayed Fab, scFv and VH libraries by panning against the receptor binding domain (RBD) of the SARS-CoV-2 spike (S) glycoprotein. One high affinity mAb, IgG1 ab1, specifically neutralized replication competent SARS-CoV-2 with exceptional potency as measured by two different assays. There was no enhancement of pseudovirus infection in cells expressing Fc? receptors at any concentration. It competed with human angiotensin-converting enzyme 2 (hACE2) for binding to RBD suggesting a competitive mechanism of virus neutralization. IgG1 ab1 potently neutralized mouse ACE2 adapted SARS-CoV-2 in wild type BALB/c mice and native virus in hACE2 expressing transgenic mice. The ab1 sequence has relatively low number of somatic mutations indicating that ab1-like antibodies could be quickly elicited during natural SARS-CoV-2 infection or by RBD-based vaccines. IgG1 ab1 does not have developability liabilities, and thus has potential for therapy and prophylaxis of SARS-CoV-2 infections. The rapid identification (within 6 days) of potent mAbs shows the value of large antibody libraries for response to public health threats from emerging microbes.