Oligonucleotides are powerful molecules for programming function and assembly. When arrayed on nanoparticle scaffolds in high density, the resulting molecules, spherical nucleic acids (SNAs), become imbued with unique properties. We used the copper-catalyzed azide-alkyne cycloaddition to graft oligonucleotides on Qβ virus-like particles to see if such structures also gain SNA-like behavior. Copper-binding ligands were shown to promote the click reaction without degrading oligonucleotide substrates. Reactions were first optimized with a small-molecule fluorogenic reporter and were then applied to the more challenging synthesis of polyvalent protein nanoparticle-oligonucleotide conjugates. The resulting particles exhibited the enhanced cellular uptake and protection from nuclease-mediated oligonucleotide cleavage characteristic of SNAs, had similar residence time in the liver relative to unmodified particles, and were somewhat shielded from immune recognition, resulting in nearly 10-fold lower antibody titers relative to unmodified particles. Oligonucleotide-functionalized virus-like particles thus provide an interesting option for protein nanoparticle-mediated delivery of functional molecules.