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We report solid-state ³⁵Cl NMR spectra in three hexachlorides, (NH₄)₂SeCl₆, (NH₄)₂TeCl₆ and Rb₂TeCl₆. The C Q (³⁵Cl) quadrupole coupling constants in the three compounds were found to be 41.4±0.1 MHz, 30.3±0.1 MHz and 30.3±0.1 MHz, respectively, some of the largest C Q (³⁵Cl) quadrupole coupling constants ever measured in polycrystalline powdered solids directly via ³⁵Cl NMR spectroscopy. The ³⁵Cl EFG tensors are axial in all three cases reflecting the C ₄ᵥ point group symmetry of the chlorine sites. ³⁵Cl NMR experiments in these compounds were only made possible by employing the WURST-QCPMG pulse sequence in the ultrahigh magnetic field of 21.1 T. ³⁵Cl NMR results agree with the earlier reported ³⁵Cl NQR values and with the complementary plane-wave DFT calculations. The origin of the very large C Q (³⁵Cl) quadrupole coupling constants in these and other main-group chlorides lies in the covalent-type chlorine bonding. The ionic bonding in the ionic chlorides results in significantly reduced C Q (³⁵Cl) values as illustrated with triphenyltellurium chloride Ph₃TeCl. The high sensitivity of ³⁵Cl NMR to the chlorine coordination environment is demonstrated using tetrachlorohydroxotellurate hydrate K[TeCl₄(OH)]∙0.5H₂O as an example. ¹²⁵Te MAS NMR experiments were performed for tellurium compounds to support ³⁵Cl NMR findings.