In analogy with photometric distance estimates for galaxies and quasars (''photo-z''), we propose photometric stellar distance estimation method, photo-D, -- that produces color-based estimates of distances for tens of billions of stars that will be observed by the Vera C. Rubin Observatory's Legacy Survey of Space and Time. This fully Bayesian procedure also produces estimates of stellar parameters such as metallicity and surface gravity, and interstellar dust extinction along the line of sight to each star. These additional LSST data products will enable studies of the Milky Way ranging from tests of models for its formation and evolution to search for stellar streams which are excellent probes of dark matter distribution. The scientific and community impact of such a publicly available catalog to accompany each LSST Data Release would be enormous: extrapolating from extant surveys such as SDSS, Pan-STARRS, DES and Gaia, it would enable many hundreds, if not thousands of papers and result in unprecedented maps of the Milky Way extending all the way to the presumed halo edge at several hundred kiloparsecs.