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We have revisited the chemistry of chlorine-bearing species in the diffuse interstellar medium with new observations of the HCl$^+$ molecular ion and new astrochemical models. Using the GREAT instrument on board SOFIA, we observed the $^2\Pi_{3/2}\, J = 5/2 - 3/2$ transition of HCl$^+$ near 1444 GHz toward the bright THz continuum source W49N. We detected absorption by diffuse foreground gas unassociated with the background source, and were able to thereby measure the distribution of HCl$^+$ along the sight-line. We interpreted the observational data using an updated version of an astrochemical model used previously in a theoretical study of Cl-bearing interstellar molecules. The abundance of HCl$^+$ was found to be almost constant relative to the related H$_2$Cl$^+$ ion, but the observed $n({\rm H_2Cl^+})/n({\rm HCl^+})$ abundance ratio exceeds the predictions of our astrochemical model by an order-of-magnitude. This discrepancy suggests that the rate of the primary destruction process for ${\rm H_2Cl^+}$, dissociative recombination, has been significantly overestimated. For HCl$^+$, the model predictions can provide a satisfactory fit to the observed column densities along the W49N sight-line while simultaneously accounting for the ${\rm OH^+}$ and ${\rm H_2O^+}$ column densities., Comment: 34 pages. 8 figures. Accepted for publication in the Astrophysical Journal