One of the interesting prospects raised by CGRO but never properly investigated due to the lack of instrumental sensitivity and resolution is the gamma-ray line emission from giant molecular clouds. In this paper, we study the 0.511 MeV annihilation line that is emitted when cosmic rays (CRs) bombarding a cloud produce radioisotopes that decay and produce positrons, which subsequently annihilate either directly or after the formation of Positronium. Several interesting factors come into play to decide whether the flux of this emission is strong enough to be detected by INTEGRAL, among them the intensity of the cosmic rays and their nuclear composition, as well as the mass, distance, and other characteristics of the molecular cloud. We have computed both the flux and the line width of the radiation for four nearby clouds. It is found that the line width can be very small (0.1 keV or less) in the case of a partially ionized cold core. This preliminary result, however, does not take into account Doppler shifts due to various motions of the cloud, as well as field-view effects, which may lead to a modification of the overall measured spectrum. We compare our preliminary results to INTEGRAL’s capabilities and conclude with the prospects for a successful detection of such a radiation. ©2001 American Institute of Physics.