Many viral surface glycoproteins and cell surface receptors are homo-oligomers, and thus can potentially be targeted by geometrically matched homo-oligomers that engage all subunits simultaneously to attain high avidity and/or lock subunits together. The adaptive immune system cannot generally employ this strategy since the individual antibody binding sites are not arranged with appropriate geometry to simultaneously engage multiple sites in a single target homo-oligomer. We describe a general strategy for the computational design of homo-oligomeric protein assemblies with binding functionality precisely matched to homo-oligomeric target sites. In the first step, a small protein is designed that binds a single site on the target. In the second step, the designed protein is assembled into a homo-oligomer such that the designed binding sites are aligned with the target sites. We use this approach to design high-avidity trimeric proteins that bind influenza A hemagglutinin (HA) at its conserved receptor binding site. The designed trimers can both capture and detect HA in a paper-based diagnostic format, neutralizes influenza in cell culture, and completely protects mice when given as a single dose 24 h before or after challenge with influenza.