Because apoptosis of infected cells can limit virus production and spread, some viruses have co-opted prosurvival genes from the host. This includes the Epstein-Barr virus (EBV) gene BHRF1, a homolog of human Bcl-2 proteins that block apoptosis and are associated with cancer. Computational design and experimental optimization were used to generate a novel protein called BINDI that binds BHRF1 with picomolar affinity. BINDI recognizes the hydrophobic cleft of BHRF1 in a manner similar to other Bcl-2 protein interactions but makes many additional contacts to achieve exceptional affinity and specificity. BINDI induces apoptosis in EBV-infected cancer lines, and when delivered with an antibody-targeted intracellular delivery carrier, BINDI suppressed tumor growth and extended survival in a xenograft disease model of EBV-positive human lymphoma. High-specificity-designed proteins that selectively kill target cells may provide an advantage over the toxic compounds used in current generation antibody-drug conjugates.