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Abstract We present the Local GroupL-Band Survey, a Karl G. Jansky Very Large Array (VLA) survey producing the highest-quality 21 cm and 1–2 GHz radio continuum images to date, for the six VLA-accessible, star-forming, Local Group galaxies. Leveraging the VLA’s spectral multiplexing power, we simultaneously survey the 21 cm line at high 0.4 km s⁻¹velocity resolution, the 1–2 GHz polarized continuum, and four OH lines. For the massive spiral M31, the dwarf spiral M33, and the dwarf irregular galaxies NGC 6822, IC 10, IC 1613, and the Wolf–Lundmark–Melotte Galaxy, we use all four VLA configurations and the Green Bank Telescope to reach angular resolutions of <5″ (10–20 pc) for the 21 cm line with <10²⁰cm⁻²column density sensitivity, and even sharper views (<2″; 5–10 pc) of the continuum. Targeting these nearby galaxies (D ≲ 1 Mpc) reveals a sharp, resolved view of the atomic gas, including 21 cm absorption, and continuum emission from supernova remnants and Hiiregions. These data sets can be used to test theories of the abundance and formation of cold clouds, the driving and dissipation of interstellar turbulence, and the impact of feedback from massive stars and supernovae. Here, we describe the survey design and execution, scientific motivation, data processing, and quality assurance. We provide a first look at and publicly release the wide-field 21 cm Hidata products for M31, M33, and four dwarf irregular targets in the survey, which represent some of the highest-physical-resolution 21 cm observations of any external galaxies beyond the LMC and SMC.