The elicitation of cross-neutralizing antibodies to the HIV-1 envelope glycoprotein (Env) by vaccination remains a major challenge. Here, we immunized previously Env-immunized nonhuman primates with a series of near-native trimers that possessed N-glycan deletions proximal to the conserved CD4 binding site (CD4bs) to focus B cells to this region. Following heterologous boosting with fully glycosylated trimers, we detected tier 2 cross-neutralizing activity in the serum of several animals. Isolation of 185 matched heavy- and light-chain sequences from Env-binding memory B cells from an early responder identified a broadly neutralizing antibody lineage, LJF-0034, which neutralized nearly 70% of an 84-member HIV-1 global panel. High-resolution cryoelectron microscopy (cryo-EM) structures revealed a bifurcated binding mode that bridged the CD4bs to V3 across the gp120:120 interface on two adjacent protomers, evading the proximal N276 glycan impediment to the CD4bs, allowing neutralization breadth. This quaternary epitope defines a potential target for future HIV-1 vaccine development.