Antibodies are widely developed and used as therapeutics to treat cancer, infectious disease, and inflammation. During development, initial leads routinely undergo additional engineering to increase their target affinity. Experimental methods for affinity maturation are expensive, laborious, and time-consuming and rarely allow the efficient exploration of the full design space. Deep learning (DL) models are transforming the field of protein structure-prediction, engineering, and design. While several DL-based protein design methods have shown promise, the antibody design problem is distinct, and specialized models for antibody design are desirable. Inspired by hallucination frameworks that leverage accurate structure prediction DL models, we propose the FvHallucinator for designing antibody sequences, especially the CDR loops, conditioned on a target antibody structure. On a benchmark set of 60 antibodies, FvHallucinator recovers over 50% of the wildtype sequence with wildtype seeding on all six CDRs and recapitulates perplexity of canonical CDR clusters. Furthermore, the FvHallucinator designs amino acid substitutions at the VH-VL interface that are enriched in human antibody repertoires and therapeutic antibodies. We propose a pipeline that screens FvHallucinator designs to obtain a library enriched in binders for an antigen of interest. We apply this pipeline to the CDR H3 of the Trastuzumab-HER2 complex to generate in silico designs that retain the original binding mode while also improving upon the binding affinity and interfacial properties of the original antibody. Thus, the FvHallucinator pipeline enables generation of inexpensive, diverse, and structure-conditioned antibody libraries enriched in binders for antibody affinity maturation.