Administration of HIV-1 neutralizing antibodies can suppress viremia and prevent infection in vivo. However, clinical use is challenged by envelope diversity and rapid viral escape. Here, we performed single B cell profiling of 32 top HIV-1 elite neutralizers to identify broadly neutralizing antibodies with highest antiviral activity. From 831 expressed monoclonal antibodies, we identified 04_A06, a VH1-2-encoded broadly neutralizing antibody to the CD4 binding site with remarkable breadth and potency against multiclade pseudovirus panels (geometric mean half-maximal inhibitory concentration = 0.059 µg ml-1, breadth = 98.5%, 332 strains). Moreover, 04_A06 was not susceptible to classic CD4 binding site escape variants and maintained full viral suppression in HIV-1-infected humanized mice. Structural analyses revealed an unusually long 11-amino-acid heavy chain insertion that facilitates interprotomer contacts with highly conserved residues on the adjacent gp120 protomer. Finally, 04_A06 demonstrated high activity against contemporaneously circulating viruses from the Antibody-Mediated Prevention trials (geometric mean half-maximal inhibitory concentration = 0.082 µg ml-1, breadth = 98.4%, 191 virus strains), and in silico modeling for 04_A06LS predicted prevention efficacy of >93%. Thus, 04_A06 will provide unique opportunities for effective treatment and prevention of HIV-1 infection.