The singlet-oxygen (1O2) quenching-reaction by vitamin E (α-tocopherol) was studied by using density functional theory, and the potential energy curve was calculated. On the basis of the computational results, the following mechanism was suggested for the quenching reaction. In the initial stage of the quenching reaction, 1O2 and α-tocopherol approach each other, a partial electron transfer takes place from α-tocopherol to 1O2, and an exciplex between the two molecules is formed. Further approach raises the potential energy of the exciplex and leads to a crossing point between the potential energy curves of the lowest singlet and triplet states. Then, physical quenching from 1O2 to 3O2 is caused by α-tocopherol. Even more approach of 1O2 and α-tocopherol yields a pseudo-stable 6,8a-endoperoxide of α-tocopherol after passing through a transition state. The 6,8a-endoperoxide could be transformed to the primary product (8a-hydroxyperoxy-α-tocopherone) of a chemical reaction between 1O2 and α-tocopherol. The geometries at the potential energy minima and the transition state in the lowest singlet state were optimized, and the geometry at the potential-energy curve crossing-point between the lowest singlet and triplet states was obtained besides stabilization and activation energies included in the potential energy curve. The geometry of the primary product of the chemical reaction was also optimized.