Cluster anions of boron are built up on three-center two-electron bonds in contrast to naturally occurring compounds and their synthetic analogs. Methanol works as a solvent and as a competing agent, which advantageously adjusts reasonable strength of their interaction with native CDs in water-organic BGE. The highest methanol concentration preserving chiral discrimination of atropoisomers of individual anions is approximately 35, 55 and 75% v/v for alpha-, beta- and gamma-CD, respectively. alpha-CD separates anionic 7, 8-nido-dicarbaundecaborate clusters with small exo-skeletal substituents. beta-CD separates anions of all four tested structural types. The efficiency of separation of a compound with alpha- or beta-CD is always markedly lower than the separation efficiency at the absence of a CD in BGE. The efficiency of separation of a compound with beta-CD is always lower than the efficiency of separation of the compound with alpha-CD. gamma-CD was proved to be unsuitable as a chiral selector because in BGEs with gamma-CD, effective mobilities of analytes as well as their differences continuously decrease. The decrease was ascribed to the decomposition of the gamma-CD. The assessment of analytical prospect of alpha- and beta-CDs as chiral selectors for chiral separations of boron cluster anions requires knowledge of stability of individual CDs at the conditions of analyses and recognition of the chance to eliminate low separation efficiency.