Elicitation of HIV broadly neutralizing antibodies (bnAbs) by vaccination first requires the activation of diverse precursors, followed by successive boosts that guide these responses to enhanced breadth through the acquisition of somatic mutations. Because HIV bnAbs contain mutations in their B cell receptors (BCRs) that are rarely generated during conventional B cell maturation, HIV vaccine immunogens must robustly engage and expand B cells with BCRs that contain these improbable mutations. Here, we engineered an immunogen that activates diverse precursors of an HIV V3-glycan bnAb and promotes their acquisition of a functionally critical improbable mutation. This immunogen was validated biochemically, structurally, and in three different humanized immunoglobulin mouse models that were designed to test HIV immunogens. These results provide a blueprint for rationally designing priming immunogens that explicitly target the elicitation of antibodies with functional yet improbable mutations.