Liquid hydrogen chloride is modeled by a System of heteronuclear two-center Lennard-Jones particles with embedded point dipoles and quadrupoles. The effect of molecular polarizability is incorporated via an effective dipole approximation. The study is performed by Monte Carlo reaction field simulation and by hypernetted chain and reference hypernetted chain integral equations. Our simulation results yield dielectric properties in excellent agreement with experimental data for liquid HCl. As for the integral equation approach, we have experimented with an empirical choice of the reference system in the spirit of a recently proposed treatment which has proved extremely successful for pure and quadrupolar two-center Lennard-Jones fluids. The hypernetted chain equation performs slightly better when accounting for the multipolar contributions to the configurational energy, but as a whole the reference hypernetted chain equation; as introduced, here proves to be a more appropriate; choice.