Through density functional theory calculations, to provide insight into the origins of the catalytic activity of Au nanoparticles (NPs) toward oxidation reactions, we have scrutinized the oxygen adsorption chemistry of 9 types of small unsupported Au NPs of around 1 nm in size (Au13, Au19, Au20, Au25, Au38, and Au55) looking at several factors (size, shape, and coordination number). We found that these NPs, except for the icosahedral Au13, do not strongly bind to O2 molecules. Energetically most feasible O2 adsorption that potentially provides high CO oxidation activity is observed in the icosahedral Au13, our smallest Au NP. In spite of the chemical inertness of bulk Au, the structural fluxionality of such very small Au NP enables strong O2 adsorption. Our results can support recent experimental findings that the exceptional catalytic activity of Au NPs comes from very small Au species consisting of around 10 atoms each.