A simple chloroalkane or chlorocycloalkane has a very small hydrogen bond basicity, B = 0.1 units. Since B is often an additive function, it is possible that polychloro-alkanes or -cycloalkanes could have quite large hydrogen bond basicities. Literature data on the 1,2,3,4,5,6-hexachlorocyclohexanes (HCHs) have been analyzed by Abraham's linear free energy relationships to obtain solvation descriptors. These are not extraordinary except for the hydrogen bond basicity, B, which is indeed very large. Values of B for the HCHs are larger than many functionally substituted aliphatic compounds and as large as that of aliphatic amines. We find that B is 0.62-0.72 for the HCHs compared to 0.45 for propanone and 0.70 for ethylamine, the first time that such large hydrogen bond basicities have been identified in compounds with no functional groups. Hydrogen bond basicities are analyzed in order to examine what types of polychlorocompounds give rise to these elevated B values.