DFT study on O₂ adsorption on a nanocrystalline titania is presented for the first time. The dioxide's nanoparticle is modeled via the nanocluster Ti₈O₁₆. According to the calculations, O₂ physisorbs on the nanocluster Ti₈O₁₆ in S⁰ and T⁰ states and chemisorbs on the nanocluster in S¹ state. The computed adsorption enthalpies, O₂ vibrational frequencies, and O₂ ⁻ g-tensor agree well with available data. In contrast to the axial O₂ orientation on a surface of titania with oxygen vacancies, in the chemisorption complex O₂ is oriented laterally. We explain this by the sterical hindrance of the Ti³⁺ centers in the former case.