This work explores the behavior of chiral compound mixtures enriched in one of the enantiomers whilst a typical chromatography on the achiral stationary phase is employed. The influence of several factors, such as the eluent composition, ratio of the compound to the stationary phase, and the initial enatiomeric purity of the compound used on the distribution of the enantiomers in the collected chromatographic fraction, was studied. The obtained results indicate that the phenomenon of Self Disproportionation of Enantiomer (SDE) occurred in all cases, and some of the collected fractions got higher optical purities than the initial one. Thus, achiral column chromatography could be applied in some cases as the simplest approach for chiral purification. Based on the experimental results and DFT calculations, an alternative concept explaining the SDE phenomenon was proposed. Due to its generality and simplicity, SDE may also be responsible for the formation of the first chiral non-racemic compounds on the early Earth.