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Nucleic acid nanoparticles (NANPs) fabricated by using the DNA origami method have broad utility in materials science and bioengineering. Their site-specific, heterovalent functionalization with secondary molecules such as proteins or fluorophores is a unique feature of this technology that drives its utility. Currently, however, there are few chemistries that enable fast, efficient covalent functionalization of NANPs with a broad conjugate scope and heterovalency. To address this need, we introduce synthetic methods to access inverse electron-demand Diels-Alder chemistry on NANPs. We demonstrate a broad conjugate scope, characterize application-relevant kinetics, and integrate this new chemistry with strain-promoted azide-alkyne cycloaddition chemistry to enable heterovalent click reactions on NANPs. We applied these chemistries to formulate a prototypical chemical countermeasure against chemical nerve agents. We envision this additional chemistry finding broad utility in the synthetic toolkit accessible to the nucleic acid nanotechnology community.