A key step in the mechanism of polar ozone depletion involves the interaction of HCl with the particles that constitute polar stratospheric clouds. These particles exist as hexagonal ice Ih crystals below approximately 185 K. As a first step, we examine the binding of molecular HCl to a number of extended surface models of the basal (0001) face of hexagonal ice in addition to a cluster model representative of an unreconstructed adsorption site. Calculations are performed using gradient-corrected density-functional theory and high-order correlation methods. After correcting for zero-point energies, we estimate the molecular binding energy and enthalpy at 185 K to be 23 and 25 kJ/mol, respectively, for low (single-molecule) HCl coverage. These estimates decrease by a few kJ/mol at higher HCl coverage and are based partially on a low density of dangling surface OH groups. Our results set the stage for future studies addressing the possible ionization of molecularly adsorbed HCl using first-principles molecular dynamics.