Using the second-order Møller–Plesset perturbation theory (MP2), together with Dunning’s all-electron correlation consistent basis set aug-cc-pVTZ, we show that the covalently bound oxygen atom present in a series of 21 prototypical monomer molecules examined does conceive a positive (or a negative) σ-hole. A σ-hole, in general, is an electron density-deficient region on a bound atom M along the outer extension of the R–M covalent bond, where R is the reminder part of the molecule, and M is the main group atom covalently bonded to R. We have also examined some exemplar 1:1 binary complexes that are formed between five randomly chosen monomers of the above series and the nitrogen- and oxygen-containing Lewis bases in N2, PN, NH3, and OH2. We show that the O-centered positive σ-hole in the selected monomers has the ability to form the chalcogen bonding interaction, and this is when the σ-hole on O is placed in the close proximity of the negative site in the partner molecule. Although the interaction energy and the various other 12 characteristics revealed from this study indicate the presence of any weakly bound interaction between the monomers in the six complexes, our result is strongly inconsistent with the general view that oxygen does not form a chalcogen-bonded interaction.