Modern theories of galaxy formation predict that the Galactic stellar halo was hierarchically assembled from the accretion and disruption of smaller systems. This hierarchical assembly is expected to produce a high degree of structure in the combined phase and chemistry space; this structure should provide a relatively direct probe of the accretion history of our Galaxy. Revealing this structure requires precise 3D positions (including distances), 3D velocities, and chemistry for large samples of stars. The Gaia satellite is delivering proper motions and parallaxes for >1 billion stars to G~20. However, radial velocities and metallicities will only be available to G~15, which is insufficient to probe the outer stellar halo (>10 kpc). Moreover, parallaxes will not be precise enough to deliver high-quality distances for stars beyond ~10 kpc. Identifying accreted systems throughout the stellar halo therefore requires a large ground-based spectroscopic survey to complement Gaia. Here we provide an overview of the H3 Stellar Spectroscopic Survey, which will deliver precise stellar parameters and spectrophotometric distances for 200,000 stars to r=18. Spectra are obtained with the Hectochelle instrument at the MMT, which is configured for the H3 Survey to deliver resolution R~23,000 spectra covering the wavelength range 5150A-5300A. The survey is optimized for stellar halo science and therefore focuses on high Galactic latitude fields (|b|>30 deg.), sparsely sampling 15,000 sq. degrees. Targets are selected on the basis of Gaia parallaxes, enabling very efficient selection of bone fide halo stars. The survey began in the Fall of 2017 and has collected 88,000 spectra to-date. All of the data, including the derived stellar parameters, will eventually be made publicly available via the survey website: h3survey.rc.fas.harvard.edu.
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