HIV-1 vaccine development aims to elicit broadly neutralizing antibodies (bnAbs) against diverse viral strains. In some HIV-1-infected individuals, bnAbs evolved from precursor antibodies through affinity maturation. To induce bnAbs, a vaccine must mediate a similar antibody maturation process. One way to test a vaccine is to immunize mouse models that express human bnAb precursors and assess whether the vaccine can convert precursor antibodies into bnAbs. A major problem with such mouse models is that bnAb expression often hinders B cell development. Such developmental blocks may be attributed to the unusual properties of bnAb variable regions, such as poly-reactivity and long antigen-binding loops, which are usually under negative selection during primary B cell development. To address this problem, we devised a method to circumvent such B cell developmental blocks by expressing bnAbs conditionally in mature B cells. We validated this method by expressing the unmutated common ancestor (UCA) of the human VRC26 bnAb in transgenic mice. Constitutive expression of the VRC26UCA led to developmental arrest of B cell progenitors in bone marrow; poly-reactivity of the VRC26UCA and poor pairing of the VRC26UCA heavy chain with the mouse surrogate light chain may contribute to this phenotype. The conditional expression strategy bypassed the impediment to VRC26UCA B cell development, enabling the expression of VRC26UCA in mature B cells. This approach should be generally applicable for expressing other bnAbs that are under negative selection during B cell development.