Summary A subset of individuals infected with HIV-1 develops broadly neutralizing antibodies (bNAbs) that can prevent infection, but it has not yet been possible to elicit these antibodies by immunization. To systematically explore how immunization might be tailored to produce them, we generated mice expressing the predicted germline or mature heavy chains of a potent bNAb to the CD4 binding site (CD4bs) on the HIV-1 envelope glycoprotein (Env). Immunogens specifically designed to activate B cells bearing germline antibodies are required to initiate immune responses, but they do not elicit bNAbs. In contrast, native-like Env trimers fail to activate B cells expressing germline antibodies but elicit bNAbs by selecting for a restricted group of light chains bearing specific somatic mutations that enhance neutralizing activity. The data suggest that vaccination to elicit anti-HIV-1 antibodies will require immunization with a succession of related immunogens.