The antibody access to some conserved structures on the HIV-1 envelope glycoprotein (Env) is sterically restricted. We have hypothesized that the smallest independently folded antibody fragments (domains) could exhibit exceptionally potent and broadly cross-reactive neutralizing activity by targeting hidden conserved epitopes that are not accessible by larger antibodies. To test this hypothesis, we constructed a large (size 2.5 × 10¹⁰), highly diversified library of human antibody variable domains (domain antibodies) and used it for selection of binders to conserved Env structures by panning sequentially against Envs from different isolates. The highest affinity binder, m36, neutralized all tested HIV-1 isolates from clades A– D with an activity on average higher than that of C34, a peptide similar to the fusion inhibitor T20, which is in clinical use, and that of m9, which exhibits a neutralizing activity superior to known potent cross-reactive antibodies. Large-size fusion proteins of m36 exhibited diminished neutralizing activity but preincubation of virions with soluble CD4 restored it, suggesting that m36 epitope is sterically restricted and induced by CD4 (CD4i). M36 bound to gp120-CD4 complexes better than to gp120 alone and competed with CD4i antibodies. M36 is the only reported representative of a promising class of potent, broadly cross-reactive HIV-1 inhibitors based on human domain antibodies. It has potential for prevention and therapy and as an agent for exploration of the closely guarded conserved Env structures with implications for design of small molecule inhibitors and elucidation of mechanisms of virus entry and evasion of immune responses.