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We describe a large simulation of the stars to be observed by the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). The simulation is based on the TRILEGAL code, which resorts to large databases of stellar evolutionary tracks, synthetic spectra, and pulsation models, added to simple prescriptions for the stellar density and star formation histories of the main structures of the Galaxy, to generate mock stellar samples through a population synthesis approach. The main bodies of the Magellanic Clouds are also included. A complete simulation is provided for single stars, down to the $r=27.5$ mag depth of the co-added wide-fast-deep survey images. A second simulation is provided for a fraction of the binaries, including the interacting ones, as derived with the BinaPSE module of TRILEGAL. We illustrate the main properties and numbers derived from these simulations, including: comparisons with real star counts; the expected numbers of Cepheids, long-period variables and eclipsing binaries; the crowding limits as a function of seeing and filter; the star-to-galaxy ratios, etc. Complete catalogs are accessible through the NOIRLab Astro Data Lab, while the stellar density maps are incorporated in the LSST metrics analysis framework (MAF).