We have computed new rate coefficients for the collisional excitation of HCI by He, in the close-coupled formalism and using an interaction potential determined recently by Willey, Choong, & DeLucia. Results have been obtained for temperatures between 10 K and 300 K. With the use of the infinite order sudden approximation, we have derived approximate expressions of general applicability which may be used to estimate how the rate constant for a transition (J --> J') is apportioned among the various hyperfine states F' of the final state J'. Using these new rate coefficients, we have obtained predictions for the HCI rotational line strengths expected from a dense clump of interstellar gas, as a function of the HCI fractional abundance. Over a wide range of HCl abundances, we have found that the line luminosities are proportional to (abundance)2/3, a general result which can be explained using a simple analytical approximation. Our model for the excitation of HCI within a dense molecular cloud core indicates that the J = 1-0 line strengths measured by Blake, Keene, & Phillips toward the Orion Molecular Cloud (OMC-1) imply a fractional abundance n(HCl)/n(H-2) approximately 2 x 10(-9), a value which amounts to only approximately 0.3% of the cosmic abundance of chlorine nuclei. Given a fractional abundance of 2 x 10(-9), the contribution of HCl emission to the total radiative cooling of a dense clump is small. For Orion, we predict a flux approximately 10(-19) W cm-2 for the HCl J = 3-2 line near 159.8 mum suggesting that the strength of this line could be measured using the Infrared Space Observatory.