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We report the ground state tunneling splittings (ΔE±) of a number of axially chiral molecules using the ring‐polymer instanton (RPI) method (J. Chem. Phys., 2011, 134, 054109). The list includes isotopomers of hydrogen dichalcogenides H2X2 (X = O, S, Se, Te, and Po), hydrogen thioperoxide HSOH and dichlorodisulfane S2Cl2. Ab initio electronic‐structure calculations have been performed on the level of second‐order Møller–Plesset perturbation (MP2) theory either with split‐valance basis sets or augmented correlation‐consistent basis sets on H, O, S, and Cl atoms. Energy‐consistent pseudopotential and corresponding triple zeta basis sets of the Stuttgart group are used on Se, Te, and Po atoms. The results are further improved using single point calculations performed at the coupled cluster level with iterative singles and doubles and perturbative triples amplitudes. When available for comparison, our computed values of ΔE± are found to lie within the same order of magnitude as values reported in the literature, although RPI also provides predictions for H2Po2 and S2Cl2, which have not previously been directly calculated. Since RPI is a single‐shot method which does not require detailed prior knowledge of the optimal tunneling path, it offers an effective way for estimating the tunneling dynamics of more complex chiral molecules, and especially those with small tunneling splittings. [ABSTRACT FROM AUTHOR]